化简sin^4x-sin^2+cos^2化简（1）sin^4x-sin^2+cos^2（2）根号（1+cosα/1-cosα)+根_数学解答

化简sin^4x-sin^2+cos^2
化简（1）sin^4x-sin^2+cos^2
（2）根号（1+cosα/1-cosα)+根号（1-cosα/1+cosα）（180°＜α＜270°）

人气：381 ℃　时间：2020-06-06 19:15:19

解答

(1) (sinx)^4 - (sinx)^2 + (cosx)^2
=(1-cos2x)^2/4 + cos2x
= [ 1 - 2 cos2x + (cos2x)^2 + 4 cos2x ] / 4
= ( 1 + cos2x )^2 /4
= [ ( 1 + cos2x ) / 2 ]^2
= (cosx)^4