Evaluate the following Integrals:

Let

As we have the trigonometric identity 1 + tan²θ = sec²θ, to evaluate this integral we use x = tan θ

⇒ dx = sec²θ dθ (Differentiating both sides)

When x = 0, tan θ = 0 ⇒ θ = 0

So, the new limits are 0 and.

Substituting this in the original integral,

We have cos²θ – sin²θ = cos 2θ