Question

$\int \frac{\tan x}{\sec x}\cos xdx$

Answer 1

$\int \frac{\tan x}{\sec x}\cos xdx\int \frac{\frac{\sin x}{\cos x}}{\frac{1}{\cos x}}\cos xdx\int \sin x\cos xdxt=\sin x⟹dt=\cos xdx\int tdt\frac{t^2}{2}+c\frac{{\sin }^{2}x}{2}+c$