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Relation between Inverses of Trigonometric Functions and Their Reciprocal Functions

∫ sin x / 2 c...

Question

$\int s i n \frac{x}{2} c o s \frac{x}{2} d x$

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Solution

$\int sin \frac{x}{2} cos \frac{x}{2} d x$

$= \frac{1}{2} \int 2 sin \frac{x}{2} cos \frac{x}{2} d x$

$= \frac{1}{2} \int sin x d x$ since $sin 2 x = 2 sin x cos x$

$= \frac{1}{2} (- cos x) + c$

$= \frac{- cos x}{2} + c$

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