化简（cos^2α-sin^2α）/2cot(π/4+α)cos^2(π/4-α)
1个回答
cos^2α-sin^2α=(cosα+sinα)(cosα-sinα)=cos2α
2cot(π/4+α)=2tan(π/4-α)=2(1-tanα)/(1+tanα)
cos^2(π/4-α)=[1+cos(π/2-2α)]/2=(1+sin2α)/2=(cosα+sinα)^2/2
2cot(π/4+α)cos^2(π/4-α)=(1-tanα)(cosα+sinα)^2/(1+tanα)
（cos^2α-sin^2α）/2cot(π/4+α)cos^2(π/4-α)
=cos2α(1+tanα)/(1-tanα)(cosα+sinα)^2 (上下乘cosα)
=cos2α(sinα+cosα)/(cosα-sinα)(cosα+sinα)^2 (上下约sinα+cosα)
=cos2α/(cosα-sinα)(cosα+sinα)
=(cosα+sinα)(cosα-sinα)/(cosα+sinα)(cosα-sinα)
=1
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