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Bentuk sederhana dari  adalah ....

Pertanyaan

Bentuk sederhana dari begin mathsize 14px style sin cubed straight theta times cotan squared straight theta end style adalah ....

  1. size 14px sin size 14px space size 14px theta 

  2. Error converting from MathML to accessible text. 

  3. Error converting from MathML to accessible text. 

  4. Error converting from MathML to accessible text. 

  5. Error converting from MathML to accessible text. 

Pembahasan Soal:

Identitas trigonometeri:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell c o tan space theta space end cell equals cell fraction numerator 1 over denominator tan space theta end fraction end cell row blank equals cell fraction numerator cos space theta over denominator sin space theta end fraction end cell end table end style 

Maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin cubed straight theta times cotan squared straight theta end cell equals cell sin cubed straight theta times fraction numerator cos squared straight theta over denominator sin squared straight theta end fraction end cell row blank equals cell fraction numerator sin cubed straight theta times cos squared straight theta over denominator sin squared straight theta end fraction end cell row blank equals cell sin space straight theta times cos squared straight theta end cell end table end style 

Jadi, Error converting from MathML to accessible text..

Oleh karena itu, tidak ada opsi jawaban yang benar.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. RGFLLIMA

Terakhir diupdate 30 April 2021

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Sederhanakan bentuk trigonometri

Pembahasan Soal:

Diketahui bentuk trigonometri fraction numerator cot open parentheses a close parentheses times sec squared open parentheses a close parentheses over denominator 1 plus cot squared open parentheses a close parentheses end fraction. Berdasarkan identitas trigonometri 1 plus cot squared open parentheses x close parentheses equals csc squared open parentheses x close parentheses maka bentuk sederhana dari trigonometri fraction numerator cot open parentheses a close parentheses times sec squared open parentheses a close parentheses over denominator 1 plus cot squared open parentheses a close parentheses end fraction yaitu
 

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cot open parentheses a close parentheses times sec squared open parentheses a close parentheses over denominator 1 plus cot squared open parentheses a close parentheses end fraction end cell equals cell fraction numerator cot open parentheses a close parentheses times sec squared open parentheses a close parentheses over denominator csc squared open parentheses a close parentheses end fraction end cell end table


Berdasarkan definisi trigonometri yaitu cot open parentheses x close parentheses equals fraction numerator cos open parentheses x close parentheses over denominator sin open parentheses x close parentheses end fraction comma space sec open parentheses x close parentheses equals fraction numerator 1 over denominator cos open parentheses x close parentheses end fraction comma space text dan  end text csc open parentheses x close parentheses equals fraction numerator 1 over denominator sin open parentheses x close parentheses end fraction maka
 

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cot open parentheses a close parentheses times sec squared open parentheses a close parentheses over denominator 1 plus cot squared open parentheses a close parentheses end fraction end cell equals cell fraction numerator cot open parentheses a close parentheses times sec squared open parentheses a close parentheses over denominator csc squared open parentheses a close parentheses end fraction end cell row cell fraction numerator cot open parentheses a close parentheses times sec squared open parentheses a close parentheses over denominator 1 plus cot squared open parentheses a close parentheses end fraction end cell equals cell fraction numerator begin display style fraction numerator up diagonal strike cos open parentheses a close parentheses end strike over denominator sin open parentheses a close parentheses end fraction end style times begin display style fraction numerator 1 over denominator begin display style stack up diagonal strike cos squared open parentheses a close parentheses end strike with cos open parentheses a close parentheses below end style end fraction end style over denominator begin display style fraction numerator 1 over denominator sin squared open parentheses a close parentheses end fraction end style end fraction end cell row cell fraction numerator cot open parentheses a close parentheses times sec squared open parentheses a close parentheses over denominator 1 plus cot squared open parentheses a close parentheses end fraction end cell equals cell fraction numerator 1 over denominator sin open parentheses a close parentheses times cos open parentheses a close parentheses end fraction divided by fraction numerator 1 over denominator sin squared open parentheses a close parentheses end fraction end cell row cell fraction numerator cot open parentheses a close parentheses times sec squared open parentheses a close parentheses over denominator 1 plus cot squared open parentheses a close parentheses end fraction end cell equals cell fraction numerator 1 over denominator up diagonal strike sin open parentheses a close parentheses end strike times cos open parentheses a close parentheses end fraction cross times stack up diagonal strike sin squared open parentheses a close parentheses end strike with sin open parentheses a close parentheses on top end cell row cell fraction numerator cot open parentheses a close parentheses times sec squared open parentheses a close parentheses over denominator 1 plus cot squared open parentheses a close parentheses end fraction end cell equals cell fraction numerator sin open parentheses a close parentheses over denominator cos open parentheses a close parentheses end fraction end cell row cell fraction numerator cot open parentheses a close parentheses times sec squared open parentheses a close parentheses over denominator 1 plus cot squared open parentheses a close parentheses end fraction end cell equals cell tan open parentheses a close parentheses end cell end table
 

Jadi bentuk sederhana dari fraction numerator cot open parentheses a close parentheses times sec squared open parentheses a close parentheses over denominator 1 plus cot squared open parentheses a close parentheses end fraction adalah tan open parentheses a close parentheses.

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Roboguru

Pembahasan Soal:

Diketahui tan squared x plus cot squared x plus 2 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell tan squared x plus cot squared x plus 2 end cell equals cell tan squared x plus cot squared x plus 1 plus 1 end cell row blank equals cell tan squared x plus 1 plus cot squared x plus 1 end cell end table

Berdasarkan identitas trigonometri yaitu tan squared x plus 1 equals sec squared x space text dan end text space cot squared x plus 1 equals csc squared x maka

table attributes columnalign right center left columnspacing 0px end attributes row cell tan squared x plus cot squared x plus 2 end cell equals cell tan squared x plus 1 plus cot squared x plus 1 end cell row blank equals cell sec squared x plus csc squared x end cell end table

Jadi berdasarkan hitungan di atas table attributes columnalign right center left columnspacing 0px end attributes row cell tan squared x plus cot squared x plus 2 end cell equals cell sec squared x plus csc squared x end cell end table.

Oleh karena itu, jawaban yang benar adalah B.

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Roboguru

Buktikanlah setiap identitas trigonometri berikut ini: 1)

Pembahasan Soal:

Ingat bahwa begin mathsize 14px style cos squared x plus sin squared x equals 1 space left right arrow space cos squared x equals 1 minus sin squared x end style. Selanjutnya, akan dibuktikan identitas trigonometri di atas sebagai berikut

begin mathsize 11px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis cos x plus sin x right parenthesis left parenthesis cos x minus sin x right parenthesis end cell row blank equals cell open parentheses cos x cross times cos x close parentheses plus open parentheses cos x cross times open parentheses negative sin x close parentheses close parentheses plus open parentheses sin x cross times cos x close parentheses plus open parentheses sin x cross times open parentheses negative sin x close parentheses close parentheses end cell row blank equals cell cos squared x minus sin x cos x plus sin x cos x minus sin squared x end cell row blank equals cell cos squared x minus sin squared x end cell row blank equals cell open parentheses 1 minus sin squared x close parentheses minus sin squared x end cell row blank equals cell 1 minus 2 sin squared x end cell end table end style  

Jadi, terbukti bahwa begin mathsize 14px style bold left parenthesis bold cos bold x bold plus bold sin bold x bold right parenthesis begin bold style left parenthesis cos x minus sin x right parenthesis end style bold equals bold 1 bold minus bold 2 bold sin to the power of bold 2 bold italic x end style 

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Buktikan:

Pembahasan Soal:

Identitas trigonometeri.

Pembuktian: fraction numerator cotan space straight x minus cos space straight x over denominator cotan space straight x end fraction equals fraction numerator cos squared straight x over denominator 1 plus sin space straight x end fraction

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cotan space straight x minus cos space straight x over denominator cotan space straight x end fraction end cell equals cell fraction numerator cotan space straight x over denominator cotan space straight x end fraction minus fraction numerator cos space straight x over denominator cotan space straight x end fraction end cell row blank equals cell 1 minus fraction numerator cos space straight x over denominator begin display style fraction numerator 1 over denominator tan space straight x end fraction end style end fraction end cell row blank equals cell 1 minus cos space straight x times tan space straight x end cell row blank equals cell 1 minus sin space straight x end cell row blank equals cell fraction numerator left parenthesis 1 minus sin space straight x right parenthesis left parenthesis 1 plus sin space straight x right parenthesis over denominator 1 plus sin space straight x end fraction end cell row blank equals cell fraction numerator 1 minus sin squared straight x over denominator 1 plus sin space straight x end fraction end cell row blank equals cell fraction numerator cos squared space straight x over denominator 1 plus sin space straight x end fraction end cell end table 

Jadii, terbukti fraction numerator cotan space straight x minus cos space straight x over denominator cotan space straight x end fraction equals fraction numerator cos squared straight x over denominator 1 plus sin space straight x end fraction 

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Jika  dan ,  maka nilai dari  adalah ....

Pembahasan Soal:

Ingat kembali:

table attributes columnalign right center left columnspacing 0px end attributes row cell cot squared space alpha minus csc squared space alpha end cell equals cell negative 1 end cell row blank blank blank end table

Diketahui table attributes columnalign right center left columnspacing 0px end attributes row cell a space cot space alpha plus b space csc space alpha end cell equals cell x squared end cell end table dan table attributes columnalign right center left columnspacing 0px end attributes row cell b space cot space alpha plus a space csc space alpha end cell equals cell y squared end cell end table, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared plus y squared end cell equals cell a space cot space alpha plus b space csc space alpha plus b space cot space alpha plus a space csc space alpha end cell row blank equals cell open parentheses a plus b close parentheses cot space alpha plus csc space alpha open parentheses a plus b close parentheses end cell row blank equals cell open parentheses a plus b close parentheses open parentheses cot space alpha plus csc space alpha close parentheses end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus y squared end cell equals cell a space cot space alpha plus b space csc space alpha minus b space cot space alpha minus a space csc space alpha end cell row blank equals cell open parentheses a minus b close parentheses cot space alpha plus csc space alpha open parentheses a minus b close parentheses end cell row blank equals cell open parentheses a minus b close parentheses open parentheses cot space alpha minus csc space alpha close parentheses end cell end table

Sehingga, diperoleh seperti berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses x to the power of 4 minus y to the power of 4 close parentheses end cell equals cell open parentheses x squared plus y squared close parentheses open parentheses x squared minus y squared close parentheses end cell row blank equals cell open parentheses a plus b close parentheses open parentheses cot space alpha plus csc space alpha close parentheses open parentheses a minus b close parentheses open parentheses cot space alpha minus csc space alpha close parentheses end cell row blank equals cell open parentheses a squared minus b squared close parentheses open parentheses cot squared space alpha minus csc squared space alpha close parentheses end cell row blank equals cell open parentheses a squared minus b squared close parentheses open parentheses negative 1 close parentheses end cell row blank equals cell b squared minus a squared end cell end table

Dengan demikian, nilai dari open parentheses x to the power of 4 minus y to the power of 4 close parentheses adalah b squared minus a squared.

Oleh karena itu, jawaban yang benar adalah C.

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