Bentuk yang ekuivalen dengan adalah ....

Pertanyaan

Bentuk yang ekuivalen dengan $begin mathsize 14px style fraction numerator 1 over denominator cot squared invisible function application x end fraction plus fraction numerator 1 over denominator csc squared invisible function application open parentheses 90 degree plus x close parentheses end fraction plus fraction numerator 1 over denominator sec squared invisible function application open parentheses 90 degree minus x close parentheses end fraction end style$ adalah ....

$sec squared x$
$csc squared invisible function application x$
$tan squared invisible function application x$
$cos squared invisible function application x$
$negative cos squared invisible function application x$

Pembahasan Soal:

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 over denominator cot squared invisible function application x end fraction end cell equals cell tan squared invisible function application x end cell row cell fraction numerator 1 over denominator csc squared invisible function application open parentheses 90 degree plus x close parentheses end fraction end cell equals cell sin squared invisible function application open parentheses 90 degree plus x close parentheses end cell row cell fraction numerator 1 over denominator sec squared invisible function application open parentheses 90 degree minus x close parentheses end fraction end cell equals cell cos squared invisible function application open parentheses 90 degree minus x close parentheses end cell end table end style$

Akibatnya, didapat hasil sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator cot squared invisible function application x end fraction plus fraction numerator 1 over denominator csc squared invisible function application open parentheses 90 degree plus x close parentheses end fraction plus fraction numerator 1 over denominator sec squared invisible function application open parentheses 90 degree minus x close parentheses end fraction end cell row blank equals cell tan squared invisible function application x plus sin squared invisible function application open parentheses 90 degree plus x close parentheses plus cos squared invisible function application open parentheses 90 degree minus x close parentheses end cell end table$

Kemudian, ingat kembali bahwa

$begin mathsize 14px style sin invisible function application open parentheses 90 degree plus x close parentheses equals cos invisible function application x cos invisible function application open parentheses 90 degree minus x close parentheses equals sin invisible function application x end style$

Dengan kata lain, didapat pula hasil sebagai berikut.

$begin mathsize 14px style sin squared invisible function application open parentheses 90 degree plus x close parentheses equals cos squared invisible function application x cos squared invisible function application open parentheses 90 degree minus x close parentheses equals sin squared invisible function application x end style$

Oleh karena itu, diperoleh perhitungan sebagai berikut.

$begin mathsize 14px style fraction numerator 1 over denominator cot squared invisible function application x end fraction plus fraction numerator 1 over denominator csc squared invisible function application open parentheses 90 degree plus x close parentheses end fraction plus fraction numerator 1 over denominator sec squared invisible function application open parentheses 90 degree minus x close parentheses end fraction equals tan squared invisible function application x plus sin squared invisible function application open parentheses 90 degree plus x close parentheses plus cos squared invisible function application open parentheses 90 degree minus x close parentheses equals tan squared invisible function application x plus cos squared invisible function application x plus sin squared invisible function application x equals tan squared invisible function application x plus 1 equals sec squared invisible function application x end style$

Jadi, jawaban yang tepat adalah A.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

M. Haidar.

Terakhir diupdate 30 April 2021