Question

三角函数证明！

证明:cos^2α(tanα+1)(tanα-1)=cos(π+2α)
和
2 sin2α
————— = —————
tanα-cotα 2sin^2α-1
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————— = —————
tanα-cotα��2sin^2α-1

Answer 1

(1)
(cosα)^2(tanα+1)(tanα-1)=cos(π+2α)
(cosα)^2(tanα+1)(tanα-1)
=(cosα)^2((tanα)^2-1)
=(cosα)^2[(sinα)^2-(cosα)^2]/(cosα)^2
=-[(cosα)^2-(sinα)^2]
=-cos2α
=cos(π+2α)

(2)
tanα-cotα
=(sinα/cosα)-(cosα/sinα)
=((sinα)^2-(cosα)^2)/[sinαcosα]
=-(cos2α)/[sinαcosα]

2 /(tanα-cotα)
=-(2sinαcosα)/(cos2α)
=-sin2α/(1-2(sinα)^2)
=sin2α/(2sin^2α-1)