Question

Jika diketahui tan x = a. Hitunglah cos 2x

Tolong.....

Answer 1

Verified answer

Bab Trigonometri
Matematika SMA Kelas X

x = p

tan p = a = a/1 → y/x

r = √(x² + y²)
  = √(1² + a²)
  = √(a² + 1)

cos 2p = cos² p - sin² p
           = (x/r)² - (y/r)²
           = (1/√(a² + 1))² - (a/√(a² + 1))²
           = 1/(a² + 1) - a²/(a² + 1)
            = (1 - a²)/(a² + 1)
            = (1 - a²) /(1 + a²)