We know that cos 2 x = 1 – sin 2 x (a 2 sin 2 x + b 2 cos 2 x) = a 2 sin 2 x + b 2 (1 – sin 2 x) = (a 2 – b 2 )sin 2 x + b 2 Let, sin 2 x = t Differentiating both sides with respect to x = sin 2x ⇒ dt = sin2x dx Use formula Again, put t = sin 2 x

Write a value of

We know that cos²x = 1 – sin²x

(a²sin²x + b²cos²x) = a²sin²x + b²(1 – sin²x)

= (a² – b²)sin²x + b²

Let, sin²x = t

Differentiating both sides with respect to x

= sin 2x

⇒ dt = sin2x dx

Use formula

Again, put t = sin²x