Question

Докажите тождество:1/cos^4x -1/cos^2x=sin^2x/cos^2x+sin^4x/cos^4x,при cos x неравном 0

Answer 1

$\frac{1}{cos^4x}-\frac{1}{cos^2x}=\frac{sin^2x}{cos^2x}+\frac{sin^4x}{cos^4x}\\\frac{1-cos^2x}{cos^4x}=\frac{sin^2xcos^2x+sin^4x}{cos^4x}\\\frac{sin^2x}{cos^4x}=\frac{sin^2x(cos^2x+sin^2x)}{cos^4x}\\cos^2x+sin^2x=1\\\frac{sin^2x}{cos^4x}=\frac{sin^2x}{cos^4x}$
Упрощали отдельно левую часть и правую часть.