Question

已知tan(α+π/4)=1/2,求(sin2α-cos2α)/(1+cos平方α)

详细过程,谢谢!

Answer 1

tan(α+π/4)=[tanα+tan(π/4)]/[1-tanαtan(π/4)]
=[tanα+1]/[1-tanα]
[tanα+1]/[1-tanα]=1/2
1-tanα=2(tanα+1)
3tanα=-1
tanα=-1/3

(sin2α-cos^2α)/(1+cos2α)
=(2sinαcosα-cos^2α)/(1+2cos^2α-1)
=(2sinαcosα-cos^2α)/(2cos^2α)
=(2sinα-cosα)/(2cosα)
=(2tanα-1)/2
=(-2*1/3-1)/2
=-5/6