Question

Используя тождество. Упростите выражение

Answer 1

1. -(1-$sin^{2} alpha$)=-$cos^{2} alpha$
2. $( sin^{2} alpha + cos^{2} alpha )^{2} =1$
3. $sin^{2} alpha +cos ^{2} alpha +2sin alpha cos alpha + sin^{2} alpha +cos ^{2} alpha -2sin alpha cos alpha$=1+1+0=2
4.$(cos ^{2}alpha -cos ^{2}alpha cos ^{2}alpha)+ sin^{4} alpha = cos ^{2}alpha(1-cos ^{2}alpha ) + sin^{4} alpha=$$cos^{2} alpha sin^{2} alpha+ sin^{4} alpha=sin^{2} alpha(cos^{2} alpha + sin^{2} alpha)= sin^{2} alpha$