Jika x sudut lancip dan tan 4x = 4/3 , maka cos kuadrat x – sin kuadrat x=… pake cara ya makasih

Cos²x – sin²x = cos(2x)

tan4x = tan(2x+2x)
= 2tan(2x) / (1 – tan²(2x))

2tan(2x) / (1 – tan²(2x)) = 4/3
3(2tan(2x)) = 4(1 – tan²(2x))

misal tan(2x) = a
3(2a) = 4(1 – a²)
6a = 4 – 4a²
4a² + 6a – 4 = 0
2a² + 3a – 2 = 0
(2a – 1)(a + 2) = 0
2a – 1 = 0
2a = 1
a = 1/2
tan(2x) = 1/2

a + 2 = 0
a = -2
tan(2x) = -2

karena sudutnya lancip, maka x positif
tan(2x) = 1/2
arc tan 1/2 ≈ 26,56°

2x = 26,56°
x = 13,28°
memenuhi

jadi, ambil yang tan(2x) = 1/2

tan(2x) = 1/2

depan = 1
samping = 2

miring = √(2² + 1²)
= √(4+1)
= √5

cos(2x) = samping/miring
= 2/√5
= 2/5 √5