Question

cos2 x - tg2 x = 1
косинус в квадрате х - тангенс в квадрате х = 1

Answer 1

$cos^2x-tan ^2 x=1\ cos^2x-left(dfrac{sin x}{cos x} right)^2 =1\ cos^2x-dfrac{sin^2 x}{cos^2 x} =1\ cos^4x-sin^2x =cos ^2 x\ cos^4 x-cos ^2x-sin^2 x=0\ cos^4x-(cos^2x+sin^2x)=0\ cos^4 x-1=0\ cos^4x=1\ cos x=-1 vee cos x=1\ boxed{x=2kpi vee x=pi + 2k pi}$