Answer
$$\int2(\cos x)^{-1/2}\sin xdx=-4\sqrt{\cos x}+C$$
Work Step by Step
$$A=\int2(\cos x)^{-1/2}\sin xdx$$
We set $a=\cos x$, then $$da=-\sin xdx$$ $$\sin xdx=-da$$
Therefore, $$A=-\int2a^{-1/2}da$$ $$A=-\frac{2a^{1/2}}{\frac{1}{2}}+C$$ $$A=-4a^{1/2}+C=-4\sqrt a+C$$ $$A=-4\sqrt{\cos x}+C$$
