Question

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

Answer 1

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

Answer 2

Соответственно, tan(x)=tg(x); cot(x)=ctg(x)