Question

Упростить выражение (sin^2x+tg^2 *sin^2x)*ctgx

Answer 1

$\left(\sin^2x+\tan^2x\sin^2x\right)\cot x=\dfrac{\left(\sin^2x+\frac{sin^4x}{cos^2x}\right)\cos x}{\sin x}=\medskip\\=\dfrac{\cos x\sin^2 x+\frac{\sin^4x}{\cos x}}{\sin x}=\dfrac{\sin^2x\left(\cos x+\frac{\sin^2x}{\cos x}\right)}{\sin x}=\medskip\\=\sin x\left(\dfrac{\cos^2x+\sin^2x}{\cos x}\right)=\dfrac{\sin x}{\cos x}=\tan x$