If , show that f(tanθ) = sin2θ.

Question

Philoid · Accepted Answer

Given

We need to prove that f(tanθ) = sin2θ.

We have

We know

However, cos²θ + sin²θ = 1

⇒ f(tanθ) = 2sinθcosθ

∴ f(tanθ) = sin2θ

Thus, f(tanθ) = sin2θ

If, show that f(tanθ) = sin2θ.