Question

1 - cos*4 a - sin*4 a/sin*4 a - 2sin*2 a + 1 Упростить выражение

Answer 1

$frac{1-Cos^{4} alpha -Sin ^{4} alpha }{Sin ^{4} alpha -2Sin ^{2} alpha +1 } = frac{(1-Cos ^{2} alpha )(1+Cos ^{2} alpha) -Sin ^{4} alpha}{(Sin ^{2} alpha -1) ^{2} }= frac{Sin ^{2} alpha (1+Cos^{2} alpha )-Sin ^{4} alpha }{Cos ^{2} alpha }=$$frac{Sin ^{2} alpha (1+Cos ^{2} alpha -Sin ^{2} alpha) }{Cos ^{2} alpha }= frac{Sin ^{2} alpha*2Cos ^{2} alpha }{Cos ^{2} alpha}=2Sin ^{2} alpha$