Power Reduction

Power reduction formula: sin²θ = (1 − cos 2θ)/2

sin2θ=1cos2θ2\sin^{2}\theta = \dfrac{1 - \cos 2\theta}{2}

sin²θ = (1 − cos 2θ)/2 trades a squared trig function for a plain cosine at double the angle. That is the whole point: a squared term cannot be integrated directly, but a cosine can, which makes this the standard first step for ∫ sin²θ dθ.

Related Power Reduction identities

Common questions

What is the sin²θ identity?

sin²θ = (1 − cos 2θ)/2 trades a squared trig function for a plain cosine at double the angle. That is the whole point: a squared term cannot be integrated directly, but a cosine can, which makes this the standard first step for ∫ sin²θ dθ.

Which identities are related to sin²θ?

sin²θ belongs to the Power Reduction group. The identities used alongside it most often are cos²θ.

Practise it

Reading a formula is not the same as recalling it under time pressure. The workspace drills Power Reduction questions in the quiz, and the triangle solver shows a worked solution for any triangle you type in.

Or browse all 45 identities in the full reference, or read the trigonometry guides for the method behind them.