Question

Hitunglah nilai eksak dari tangen 15 derajat

Answer 1

Verified answer

Materi : Selisih Sudut Trigonometri

Pembahasan :
Tan 15°
= Tan (45 - 30)°
= (Tan 45° - Tan 30°)/(1 + Tan 45° . Tan 30°)
= (1 - 1/3√3)/(1 + 1 . 1/3√3)
= (1 - 1/3√3)/(1 + 1/3√3)
= (3 - √3)/(3 + √3)
= (3 - √3)/(3 + √3) . (3 - √3)/(3 - √3)
= (9 + 3 - 6√3)/(9 - 3)
= (12 - 6√3)/6
= 2 - √3

Answer 2

Verified answer

Caranya erick udah bener, ini alternatif cara

tan(15)
=tan(30/2)
=akar[ (1-cos(30)) / (1+cos(30))]
=akar[ (1-akar(3)/2) / (1+akar(3)/2)]
=akar[ (2-akar(3)) / (2+akar(3))]
=akar[ (2-akar(3)) / (2+akar(3)) * (2-akar(3))/(2-akar(3))]
=akar[ (2-akar(3))^2 / (4-3)]
=akar[ (2-akar(3))^2]
=2-akar(3)