求证：若tan^2 θ=tan^2 α+sec^2 α.则cos2α-2cos2θ=1
问题描述：
求证：若tan^2 θ=tan^2 α+sec^2 α.则cos2α-2cos2θ=1
答
因sec^2 α=1+tan^2 α
所以tan^2 θ=2*tan^2 α+1
(sin(θ)/cos(θ))^2=2(sin(α)/cos(α))^2+1
(1-cos^2(θ))/cos^2(θ)=2(1-cos^2(α))/cos^2(α)+1
cos^2(α)=2cos^2θ
将cos^2(α)=(1+cos(2α))/2带入上式化简即得
cos2α-2cos2θ=1