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Pertanyaan

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

Jika tan⁡(2x – 45°) = a dan tan⁡(x + 15°) = b, begin mathsize 14px style ab not equal to open curly brackets 1 comma negative 1 comma square root of 2 comma negative square root of 2 close curly brackets end style , maka tan⁡(3x – 30°)  tan⁡(x – 60°) = ....

  1. 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 

  2. 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 

  3. 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 

  4. 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 

  5. 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 

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

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.

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