Question

Solve the equation: 2 sin^2 x - 3 sin x cos x + 3 cos^2 x = 1.​

Answer 1

Answer:

We have, (sin x + sin 3x) – 3 sin 2x = (cos x + cos 3x) – 3 cos 2x

⇒ 2 sin 2x cos x – 3 sin 2x = 2 cos 2x.cos x – 3 cos 2x

⇒ sin 2x(2 cos x – 3) = cos 2x(2 cos x – 3)

⇒ sin 2x = cos 2x (As cos x ≠ 3/2)

⇒ tan 2x = 1    ⇒ tan 2x = tan π/4

⇒ 2x = nπ + π/4 , n∈Z

x = nπ/2 +π/8 , n∈Z

may this can help u

Step-by-step explanation: