Question

не могу решить помогите пожалуиста. #334. 1,2,3,4.

Answer 1

$displaystyle 1)~ cos^2alpha +frac{tg^2alpha -1}{tg^2alpha +1} =cos^2alpha +frac{sin^2alpha -cos^2alpha }{sin^2alpha +cos^2alpha }=cos^2alpha +sin^2alpha -\ -cos^2 alpha =sin^2alpha$

$2)~ displaystyle sin^2varphi +frac{ctg^2varphi -1}{ctg^2varphi +1}=sin^2varphi +frac{cos^2varphi -sin^2varphi }{cos^2varphi +sin^2varphi } =sin^2varphi +cos^2varphi -\ -sin^2varphi =cos^2varphi$

$3)~ displaystyle frac{ctg^2gamma-1}{ctg^2gamma+1}-cos^2gamma=frac{cos^2gamma-sin^2gamma}{cos^2gamma+sin^2gamma} -cos^2gamma=cos^2gamma-sin^2gamma-\ -cos^2gamma=-sin^2gamma$

$4)~displaystyle frac{tg^2x-1}{tg^2x+1}-sin^2x=frac{sin^2x-cos^2x}{sin^2x+cos^2x}-sin^2x=sin^2x-cos^2x-\ -sin^2x=-cos^2x$