Question

Find $\int {\sin }^2\frac{x}{2}-{\cos }^2\frac{x}{2}dx$

Answer 1

$\int \left[{\sin }^2\right(x/2)-{\cos }^2(x/2\left)\right]dx$

$=\int -\cos xdx({\cos }^2\theta ={\cos }^2\theta -{\sin }^2\theta )$

$=-\sin x+c$

$\therefore \int ({\sin }^2\frac{x}{2}-{\cos }^2\frac{x}{2})dx=-\sin x+C$