New kid on the Block
cosx^2/(1+tanx)=(1-tanx^2)/(1+tanx^2)(1+tanx)=(1-tanx)/(1+tan^2x)=(1-tanx)/secx^2=cosx^2-tanx/secx=(cos2x+1)/2-1/2(2sinxcosx)=1/4sin2x+x-1/2sin2x=1/4sin2x+x-1/4(-cos2x)=1/4sin2x+x+1/4sin2x
cosx^2/(1+tanx)=(1-tanx^2)/(1+tanx^2)(1+tanx)=(1-tanx)/(1+tan^2x)=(1-tanx)/secx^2=cosx^2-tanx/secx=(cos2x+1)/2-1/2(2sinxcosx)=1/4sin2x+x-1/2sin2x=1/4sin2x+x-1/4(-cos2x)=1/4sin2x+x+1/4sin2x
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