Question

помогите 458(1-4) пожалуйста!!!

Answer 1

$\cos^42x-\sin^42x=(\cos^22x-\sin^22x)(\cos^22x+\sin^22x)= \\\ =\cos^22x-\sin^22x=\cos4x$

$\frac{\cos2 \alpha }{\cos \alpha } - \frac{\sin2 \alpha }{\sin \alpha } = \frac{2\cos^2 \alpha-1 }{\cos \alpha } - \frac{2\sin \alpha\cos \alpha }{\sin \alpha } = \frac{2\cos^2 \alpha }{\cos \alpha }- \frac{1}{\cos \alpha }- 2\cos \alpha = \\\ = 2\cos \alpha - \frac{1}{\cos \alpha }- 2\cos \alpha =- \frac{1}{\cos \alpha }$

$1+\cos2x+2\sin^2x=\cos^2x+\sin^2x+\cos^2x-\sin^2x+2\sin^2x= \\\ =2\cos^2x+2\sin^2x=2$

$2\sin^2 \alpha -1=2\sin^2 \alpha -\sin^2 \alpha -\cos^2 \alpha =\sin^2 \alpha -\cos^2 \alpha =-\cos2 \alpha$