Question

设tan(θ/2)=t,证明sinθ=2t/1+t^2

Answer 1

由倍角公式得到：tanθ=2t/（1+t^2)

sinθ/cosθ=2t/(1+t^2)

sin^2θ/(1-sin^2θ)=4t^2/(1+t^2)^2

解之得：sinθ=2t/(1+t^2)