Question

Evaluate $\int \frac{{\sin }^{2}x}{1+\cos x}dx$.

Answer 1

We need to find the value of $\int \frac{{\sin }^{2}x}{1+cosx}dx$

We know that ${\sin }^{2}x+{\cos }^{2}x=1$

$⟹{\sin }^{2}x=1-{\cos }^{2}x=(1-\cos x)(1+\cos x)$

$\therefore \int \frac{{\sin }^{2}x}{1+cosx}dx=\int \frac{(1-cosx)(1+cosx)}{1+cosx}dx$

$=\int (1-cosx)dx=x-sinx+c$ , where $c$ is a constant

Therefore $\int \frac{{\sin }^{2}x}{1+cosx}dx=x-sinx+c$