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Diketahui 0° < α < 180°. Jika tanα=1+tan14∘1−tan14∘​, maka α =  ....

Pertanyaan

Diketahui 0° < α < 180°. Jika begin mathsize 14px style tan invisible function application alpha equals fraction numerator 1 minus tan invisible function application 14 degree over denominator 1 plus tan invisible function application 14 degree end fraction end style, maka α =  ....

  1. 31°

  2. 59°

  3. 121°

  4. 149°

  5. 163°

M. Mariyam

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Perhatikan bahwa tan 45° = 1 , sehingga

begin mathsize 14px style tan invisible function application alpha equals fraction numerator 1 minus tan invisible function application 14 degree over denominator 1 plus tan invisible function application 14 degree end fraction tan invisible function application alpha equals fraction numerator 1 minus tan invisible function application 14 degree over denominator 1 plus 1 times tan invisible function application 14 degree end fraction tan invisible function application alpha equals fraction numerator tan invisible function application 45 degree minus tan invisible function application 14 degree over denominator 1 plus tan invisible function application 45 degree tan invisible function application 14 degree end fraction end style 

Karena begin mathsize 14px style fraction numerator tan invisible function application A minus tan invisible function application B over denominator 1 plus tan invisible function application A tan invisible function application B end fraction equals tan invisible function application open parentheses A minus B close parentheses end style, maka

begin mathsize 14px style tan invisible function application alpha equals fraction numerator tan invisible function application 45 degree minus tan invisible function application 14 degree over denominator 1 plus tan invisible function application 45 degree tan invisible function application 14 degree end fraction tan invisible function application alpha equals tan invisible function application open parentheses 45 degree minus 14 degree close parentheses tan invisible function application alpha equals tan invisible function application 31 degree end style 

Karena 0° < α < 180° , maka α = 31° .

Jadi, jawaban yang tepat adalah A.

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