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Perhatikan kesamaan-kesamaan trigonometri berikut! i)    (1+cosx )(1−cosx ) = sin2x ii)    (secx+1)(secx−1)=tan2x iii)    (1−cscx )(cscx+1)=cot2x Kesamaan yang terbukti BENAR untuk setiap nilai x ditunjukkan oleh nomor ....

Pertanyaan

Perhatikan kesamaan-kesamaan trigonometri berikut!

i)    begin mathsize 14px style left parenthesis 1 plus cos invisible function application x space right parenthesis left parenthesis 1 minus cos invisible function application x space right parenthesis space equals space sin squared invisible function application x end style

ii)    begin mathsize 14px style left parenthesis sec invisible function application x plus 1 right parenthesis left parenthesis sec invisible function application x minus 1 right parenthesis equals tan squared x end style

iii)    begin mathsize 14px style left parenthesis 1 minus csc invisible function application x space right parenthesis left parenthesis csc invisible function application x plus 1 right parenthesis equals cot squared invisible function application x end style

Kesamaan yang terbukti BENAR untuk setiap nilai begin mathsize 14px style x end style ditunjukkan oleh nomor ....

  1. i) saja

  2. iii) saja

  3. i) dan ii) saja

  4. ii) dan iii) saja

  5. i), ii), dan iii)

F. Freelancer9

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Perhatikan kesamaan i).

i)    begin mathsize 14px style left parenthesis 1 plus cos invisible function application x space right parenthesis left parenthesis 1 minus cos invisible function application x space right parenthesis space equals space sin squared invisible function application x end style

Perhatikan bentuk pada ruas kiri.
begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 1 plus cos invisible function application x close parentheses open parentheses 1 minus cos invisible function application x close parentheses end cell equals cell 1 squared minus open parentheses cos invisible function application x close parentheses squared end cell row blank equals cell 1 minus cos squared invisible function application x end cell end table end style

Karena begin mathsize 14px style sin squared invisible function application x plus cos squared invisible function application x equals 1 end style, maka begin mathsize 14px style 1 minus cos squared invisible function application x equals sin squared invisible function application x end style.

Oleh karena itu, didapatkan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 1 plus cos invisible function application x close parentheses open parentheses 1 minus cos invisible function application x close parentheses end cell equals cell 1 minus cos squared invisible function application x end cell row blank equals cell sin squared invisible function application x end cell end table end style

Karena didapat begin mathsize 14px style open parentheses 1 plus cos invisible function application x close parentheses open parentheses 1 minus cos invisible function application x close parentheses equals sin squared invisible function application x end style, maka kesamaan i) terbukti BENAR.

 

Perhatikan kesamaan ii).

ii)   begin mathsize 14px style left parenthesis sec invisible function application x plus 1 right parenthesis left parenthesis sec invisible function application x minus 1 right parenthesis equals tan squared x end style

Perhatikan bentuk pada ruas kiri.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses sec invisible function application x plus 1 close parentheses open parentheses sec invisible function application x minus 1 close parentheses end cell equals cell open parentheses sec invisible function application x close parentheses squared minus 1 squared end cell row blank equals cell sec squared invisible function application x minus 1 end cell end table end style

Karena begin mathsize 14px style tan squared invisible function application x plus 1 equals sec squared invisible function application x end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses sec invisible function application x plus 1 close parentheses open parentheses sec invisible function application x minus 1 close parentheses end cell equals cell sec squared invisible function application x minus 1 end cell row blank equals cell open parentheses tan squared invisible function application x plus 1 close parentheses minus 1 end cell row blank equals cell tan squared invisible function application x end cell end table end style

Karena didapat begin mathsize 14px style open parentheses sec invisible function application x plus 1 close parentheses open parentheses sec invisible function application x minus 1 close parentheses equals tan squared invisible function application x end style, maka kesamaan ii) terbukti BENAR.

 

Perhatikan kesamaan iii).

iii)    begin mathsize 14px style left parenthesis 1 minus csc invisible function application x space right parenthesis left parenthesis csc invisible function application x plus 1 right parenthesis equals cot squared invisible function application x end style

Perhatikan bentuk pada ruas kiri.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 1 minus csc invisible function application x close parentheses open parentheses csc invisible function application x plus 1 close parentheses end cell equals cell open parentheses 1 minus csc invisible function application x close parentheses open parentheses 1 plus csc invisible function application x close parentheses end cell row blank equals cell 1 squared minus open parentheses csc invisible function application x close parentheses squared end cell row blank equals cell 1 minus csc squared invisible function application x end cell end table end style

Karena undefined, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 1 minus csc invisible function application x close parentheses open parentheses csc invisible function application x plus 1 close parentheses end cell equals cell 1 minus csc squared invisible function application x end cell row blank equals cell 1 minus open parentheses cot squared invisible function application x plus 1 close parentheses end cell row blank equals cell negative cot squared invisible function application x end cell end table end style

Karena didapat begin mathsize 14px style left parenthesis 1 minus csc invisible function application x space right parenthesis left parenthesis csc invisible function application x plus 1 right parenthesis equals cot squared invisible function application x end style, maka kesamaan iii) tidak terbukti BENAR.

 

Oleh karena itu, kesamaan yang terbukti BENAR untuk setiap nilai begin mathsize 14px style x end style ditunjukkan oleh nomor i) dan ii) saja.

 

Jadi, jawaban yang tepat adalah C.

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