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