已知sin(α+β)sin(α-β)=1/3.（1）求cos2β-cos2α的值；（2)求(1/4)(sin2α)^2+(sinβ_数学解答

已知sin(α+β)sin(α-β)=1/3.（1）求cos2β-cos2α的值；（2)求(1/4)(sin2α)^2+(sinβ)^2+(cosα)^4
已知sin(α+β)sin(α-β)=1/3.（1）求cos2β-cos2α的值；（2）求(1/4)(sin2α)^2+(sinβ)^2+(cosα)^4的值.
（1）2/3；（2）2/3.

人气：188 ℃　时间：2020-02-05 12:26:36

解答

(1)因为sin(α+β)sin(α-β)=1/3而cos2β-cos2α=-2*sin(α+β)sin(β-α)=2sin(α+β)sin(α-β)=2/3(2)(1/4)(sin2α)^2+(sinβ)^2+(cosα)^4=1/4*(1-cos^2(2α))+(1-cos2β)/2+[(1+cos(2α))/2]^2=1/4+(1-cos2β)...