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.