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Pertanyaan

tan 7 5 ∘ + tan 1 5 ∘ = ....

 

  1. 1space space

  2. 2space space

  3. 3space space

  4. 4space space

  5. 5space space

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N. Sari

Master Teacher

Mahasiswa/Alumni Universitas Nasional

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

jawaban yang benar adalah D.

Pembahasan

Sifat penjumlahan dan pengurangan trigonometri : Sifat perkalian trigonometri : Dengan menggunakan sifat tersebut, maka : Maka, . Oleh karena itu, jawaban yang benar adalah D.

Sifat penjumlahan dan pengurangan trigonometri :

sin space straight A plus sin space straight B equals 2 sin 1 half left parenthesis straight A plus straight B right parenthesis cos 1 half left parenthesis straight A minus straight B right parenthesis sin space straight A minus sin space straight B equals 2 cos 1 half left parenthesis straight A plus straight B right parenthesis sin 1 half left parenthesis straight A minus straight B right parenthesis cos space straight A plus cos space straight B equals 2 cos 1 half left parenthesis straight A plus straight B right parenthesis cos 1 half left parenthesis straight A minus straight B right parenthesis cos space straight A minus cos space straight B equals 2 sin 1 half left parenthesis straight A plus straight B right parenthesis sin 1 half left parenthesis straight A minus straight B right parenthesis 

Sifat perkalian trigonometri :

2 sin space straight A space cos space straight B equals sin left parenthesis straight A plus straight B right parenthesis plus sin left parenthesis straight A minus straight B right parenthesis 2 cos space straight A space sin space straight B equals sin left parenthesis straight A plus straight B right parenthesis minus sin left parenthesis straight A minus straight B right parenthesis 2 cos space straight A space cos space straight B equals cos left parenthesis straight A plus straight B right parenthesis plus cos left parenthesis straight A minus straight B right parenthesis minus 2 sin space straight A space sin space straight B equals cos left parenthesis straight A plus straight B right parenthesis plus cos left parenthesis straight A minus straight B right parenthesis 

Dengan menggunakan sifat tersebut, maka :

tan space 75 degree plus tan space 15 degree equals fraction numerator sin space 75 degree over denominator cos space 75 degree end fraction plus fraction numerator sin space 15 degree over denominator cos space 15 degree end fraction equals fraction numerator sin space 75 degree cos space 15 degree plus sin space 15 degree cos space 75 degree over denominator cos space 75 degree cos space 15 degree end fraction equals fraction numerator 1 half open parentheses 2 sin space 75 degree cos space 15 degree close parentheses plus 1 half open parentheses 2 cos space 75 degree sin space 15 degree close parentheses over denominator 1 half open parentheses 2 cos space 75 degree cos space 15 degree close parentheses end fraction equals fraction numerator 1 half open parentheses sin space 90 degree plus sin space 60 degree close parentheses plus 1 half open parentheses sin space 90 degree minus sign sin space 60 degree close parentheses over denominator 1 half open parentheses cos space 90 degree plus cos space 60 degree close parentheses end fraction equals fraction numerator 1 half open parentheses 1 plus 1 half square root of 3 close parentheses plus 1 half open parentheses 1 minus sign 1 half square root of 3 close parentheses over denominator 1 half open parentheses 0 plus 1 half close parentheses end fraction equals fraction numerator 1 half plus 1 fourth square root of 3 plus 1 half minus sign 1 fourth square root of 3 over denominator 1 fourth end fraction equals fraction numerator 1 half plus 1 half plus 1 fourth square root of 3 minus sign 1 fourth square root of 3 over denominator 1 fourth end fraction equals fraction numerator 1 over denominator 1 fourth end fraction equals 4 

Maka, tan space 75 degree plus tan space 15 degree equals 4

Oleh karena itu, jawaban yang benar adalah D.

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