If, show that f(tanθ) = sin2θ.

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


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