Question

Докажите тождество sin^2x/ctg^2x-cos^2x=tg^4x.​

Answer 1

Объяснение:

$dfrac{sin^2x}{{rm ctg}^2x-cos^2x}=dfrac{sin^2xcdot sin^2x}{cos^2x-sin^2xcos^2x}=dfrac{sin^4x}{cos^2x(1-sin^2x)}=\ \ \ =dfrac{{rm tg}^2xsin^2x}{cos^2x}={rm tg}^2xcdot{rm tg}^2x={rm tg}^4x$