Question

设tan(θ/2)=t,求证：sinθ=2t/(1+t^2),cosθ=(1-t^2)/(1+t^2),tanθ=2t/

Answer 1

下面sin,cos均指sin(θ/2),cos(θ/2)

sinθ=2sincos/(cos^2+sin^2) (上下同除cos^2)

=2t/(1+t^2)

cosθ=(cos^2-sin^2)/(cos^2+sin^2)

=(1-t^2)/(1+t^2)

tanθ=sinθ/cosθ=2t/(1-t^2)

万能公式的证明而已……