數學 M2 三角學?

Sol
(a)
Sinθ=2Sin(θ/2)Cos(θ/2)
=2Sin(θ/2)Cos(θ/2)/[Cos^2 (θ/2)+Sin^2 (θ/2)]
=[2Sin(θ/2)Cos(θ/2)/Cos^2 (θ/2)]/[Cos^2 (θ/2)/Cos^2 (θ/2)
+Sin^2 (θ/2)/Cos^2 (θ/2)]
=2Tan(θ/2)/[1+Tan^2 (θ/2)[
=2t/(1+t^2)
(b)
p=(1-t)^2/(1+t^2)=(t^2-2t+1)/(1+t^2)=1－Sinθ
－1<=－Sinθ<=1
0<=1－Sinθ<=2
0<=p<=2