СРОЧНО!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!упростите выражение (1-cos^4...

Question

СРОЧНО!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!упростите выражение
(1-cos^4 альфа-sin^4 альфа)/sin^4 альфа-2sin^2 альфа+1

Answer 1

1-cos^4a-sin^4a=1-(1+cos2a)²/4-(1-cos2a)²/4=
=1-1/4-1/2*cos2a-1/4*cos²2a-1/4+1/2*cos2a-1/4*cos²2a)=
=1/2-1/2*cos²2a=1/2*(1-cos²2a)

sin^4a-2sin²2a+1=(1-sin²a)²=cos^4a=(1-cos2a)²/4

(1-cos2a)(1+cos2a)/2:(1-cos2a)/4=(1-cos2a)(1+cos2a)/2 *4/(1-cos2a)=
=2(1+cos2a)=2*2cos²a=4cos²a