Pertanyaan

Jika tan⁡(2x – 45°) = a dan tan⁡(x + 15°) = b, , maka tan⁡(3x – 30°) tan⁡(x – 60°) = ....

$begin mathsize 14px style fraction numerator straight a squared minus straight b squared over denominator 1 plus straight a squared straight b squared end fraction end style$
$begin mathsize 14px style fraction numerator straight a squared plus straight b squared over denominator 1 minus straight a squared straight b squared end fraction end style$
$begin mathsize 14px style fraction numerator straight a squared minus straight b squared over denominator 1 minus 2 straight a squared straight b squared end fraction end style$
$begin mathsize 14px style fraction numerator straight a squared minus straight b squared over denominator 1 minus straight a squared straight b squared end fraction end style$
$begin mathsize 14px style fraction numerator straight a squared plus straight b squared over denominator 1 plus 2 straight a squared straight b squared end fraction end style$

R. Rohmat

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Perhatikan bahwa dan Sehingga Jadi, jawaban yang tepat adalah D.

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan invisible function application open parentheses 3 straight x minus 30 degree close parentheses end cell equals cell tan invisible function application open parentheses open parentheses 2 straight x minus 45 degree close parentheses plus open parentheses straight x plus 15 degree close parentheses close parentheses end cell row blank equals cell fraction numerator tan invisible function application open parentheses 2 straight x minus 45 degree close parentheses plus tan invisible function application open parentheses straight x plus 15 degree close parentheses over denominator 1 minus tan invisible function application open parentheses 2 straight x minus 45 degree close parentheses tan invisible function application open parentheses straight x plus 15 degree close parentheses end fraction end cell row blank equals cell fraction numerator straight a plus straight b over denominator 1 minus ab end fraction end cell end table end style$

dan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan invisible function application open parentheses straight x minus 60 degree close parentheses end cell equals cell tan invisible function application open parentheses open parentheses 2 straight x minus 45 degree close parentheses minus open parentheses straight x plus 15 degree close parentheses close parentheses end cell row blank equals cell fraction numerator tan invisible function application open parentheses 2 straight x minus 45 degree close parentheses minus tan invisible function application open parentheses straight x plus 15 degree close parentheses over denominator 1 plus tan invisible function application open parentheses 2 straight x minus 45 degree close parentheses tan invisible function application open parentheses straight x plus 15 degree close parentheses end fraction end cell row blank equals cell fraction numerator straight a minus straight b over denominator 1 plus ab end fraction end cell end table end style$

Sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan invisible function application open parentheses 3 straight x minus 30 degree close parentheses tan invisible function application open parentheses straight x minus 60 degree close parentheses end cell equals cell fraction numerator straight a plus straight b over denominator 1 minus ab end fraction times fraction numerator straight a minus straight b over denominator 1 plus ab end fraction end cell row blank equals cell fraction numerator straight a squared minus straight b squared over denominator 1 squared minus open parentheses ab close parentheses squared end fraction end cell row blank equals cell fraction numerator straight a squared minus straight b squared over denominator 1 minus straight a squared straight b squared end fraction end cell end table end style$

Jadi, jawaban yang tepat adalah D.