Question

(cos^4 x + sin^2 x *cos^2 x)/(1- sin^4 x - sin^2 x * cos^2 x)=?
(1-2cos^2 х)/(sin x- cos x)= ?

Answer 1

1) $frac{Cos ^{4} x + Sin ^{2}xCos ^{2}x }{1 - Sin ^{4}x - Sin ^{2}xCos ^{2}x } = frac{Cos ^{2}x(Cos ^{2}x + Sin ^{2}x) }{1 - Sin ^{2}x(Sin ^{2}x + Cos ^{2} x) } = frac{Cos ^{2}x }{1 - Sin ^{2}x } = frac{Cos ^{2}x }{Cos ^{2}x } = 1$
2) $frac{1-2Cos ^{2}x }{Sinx - Cosx} = frac{Sin ^{2}x + Cos ^{2}x - 2Cos ^{2}x }{Sinx - Cosx} = frac{Sin ^{2}x - Cos ^{2} x }{Sinx - Cosx} =$$frac{(Sinx - Cosx)(Sinx + Cosx)}{Sinx - Cosx} = Sinx + Cosx$