diketahui tanx=a, maka cos2x adalah...

Bab Trigonometri
Matematika SMA Kelas X

x = p
tan p = a/1 → y/x

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

cos 2x = 2 . cos² x - 1
cos 2x = 2 . (x/r)² - 1
cos 2x = 2 . (1/√(1 + a²))² - 1
cos 2x = 2 . (1/(1 + a²) - 1
cos 2x = (2 - 1 - a²)/(1 + a²)
cos 2x = (1 - a²) / (1 + a²)

Matematika X SMA
→→ Trigonometri ←←

Pembahasan :
Tan x = a/1

Depan = a
Samping = 1
Miring = √[a² + 1]

Maka...
Cos 2x
= Cos²x - Sin²x
= (1/√[a² + 1])² - (a/√[a² + 1])²
= 1/(a² + 1) - [a²/(a² + 1)]
= (1 - a²)/(a² + 1)
= -(a² - 1)/(a² + 1)