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Diketahui nilai cos ( α − β ) = 3 2 ​ dan cos α cos β = 2 1 ​ . Jika ( α + β ) lancip, maka tan ( α + β ) adalah...

Diketahui nilai  dan . Jika  lancip, maka  adalah... 

  1. 1 fourth square root of 2 

  2. 1 half 

  3. 2 over 3 square root of 2 

  4. 2 

  5. 2 square root of 2 

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E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.

jawaban yang benar adalah E. 

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Pembahasan

Berdasarkan rumus selisih dua sudut pada cosinus, diperoleh Menentukan Menentukan menggunakan identitas trigonometri Menentukan Jadi, jawaban yang benar adalah E.

Berdasarkan rumus selisih dua sudut pada cosinus, diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell cos left parenthesis alpha minus beta right parenthesis end cell equals cell 2 over 3 end cell row cell cos space alpha space cos space beta plus sin space alpha space sin space beta end cell equals cell 2 over 3 end cell row cell 1 half plus sin space alpha space sin space beta end cell equals cell 2 over 3 end cell row cell sin space alpha space sin space beta end cell equals cell 2 over 3 minus 1 half end cell row cell sin space alpha space sin space beta end cell equals cell 4 over 6 minus 3 over 6 end cell row cell sin space alpha space sin space beta end cell equals cell 1 over 6 end cell end table 

Menentukan cos space left parenthesis alpha plus beta right parenthesis 

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space left parenthesis alpha plus beta right parenthesis end cell equals cell cos space alpha space cos space beta minus sin space alpha space sin space beta end cell row blank equals cell 1 half minus 1 over 6 end cell row blank equals cell 3 over 6 minus 1 over 6 end cell row blank equals cell 2 over 6 end cell row blank equals cell 1 third end cell end table 

Menentukan sin space left parenthesis alpha plus beta right parenthesis menggunakan identitas trigonometri

table attributes columnalign right center left columnspacing 0px end attributes row cell sin squared space left parenthesis alpha plus beta right parenthesis plus cos squared space left parenthesis alpha plus beta right parenthesis end cell equals 1 row cell sin squared space left parenthesis alpha plus beta right parenthesis end cell equals cell 1 minus cos squared space left parenthesis alpha plus beta right parenthesis end cell row cell sin squared space left parenthesis alpha plus beta right parenthesis end cell equals cell 1 minus left parenthesis 1 third right parenthesis squared space end cell row cell sin squared space left parenthesis alpha plus beta right parenthesis end cell equals cell 1 minus 1 over 9 end cell row cell sin squared space left parenthesis alpha plus beta right parenthesis end cell equals cell 8 over 9 end cell row cell sin space left parenthesis alpha plus beta right parenthesis end cell equals cell square root of 8 over 9 end root end cell row cell sin space left parenthesis alpha plus beta right parenthesis end cell equals cell 1 third square root of 8 end cell row cell sin space left parenthesis alpha plus beta right parenthesis end cell equals cell 1 third times 2 square root of 2 end cell row cell sin space left parenthesis alpha plus beta right parenthesis end cell equals cell 2 over 3 square root of 2 end cell end table  

Menentukan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell tan space left parenthesis alpha plus beta right parenthesis end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space left parenthesis alpha plus beta right parenthesis end cell equals cell fraction numerator sin space left parenthesis alpha plus beta right parenthesis over denominator cos space left parenthesis alpha plus beta right parenthesis end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 2 square root of 2 over denominator 3 end fraction end style over denominator begin display style 1 third end style end fraction end cell row blank equals cell fraction numerator 2 square root of 2 over denominator 3 end fraction times 3 over 1 end cell row blank equals cell 2 square root of 2 end cell end table 

Jadi, jawaban yang benar adalah E. 

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