Question

Доказать тождество....

Answer 1

$a) sin^4 frac{ alpha }{2} -cos^4frac{ alpha }{2} =-cos alpha \ \ (sin^2frac{ alpha }{2} -cos^2frac{ alpha }{2} )(sin^2frac{ alpha }{2} +cos^2frac{ alpha }{2} )=-cos alpha \ \ (sin^2frac{ alpha }{2} -cos^2frac{ alpha }{2} )*1=-cos alpha \ \ -(cos^2frac{ alpha }{2}-sin^2frac{ alpha }{2})=-cosa \ \ -cos alpha =-cos alpha \ \ b) 4sin^4 alpha +sin^22 alpha =4sin^2 alpha \ \ 4sin^4 alpha+4sin ^2alpha *cos^2 alpha =4sin^2alpha$

$4sin^2 alpha (sin^2 alpha +cos^2 alpha )=4sin^2 alpha \ \ 4sin^2 alpha =4sin^2 alpha$