1》show that the identity :tanAcscA=tanAsinA+cosA is ture for π/3

题目

1》show that the identity :tanAcscA=tanAsinA+cosA is ture for π/3
2》prove the following:sin{3π/2 - θ}=-cosθ

答案

1）tanA=tan(π/3)=3^0.5 cscA=csc(π/3)=2/3^0.5 sinA=sin(π/3)=3^0.5/2 cosA=cos(π/3)=1/2
tanAcscA=3^0.5*2/3^0.5 =2 tanAsinA+cosA=3^0.5*3^0.5/2 +1/2=2 so the identity is true
2）sin{3π/2 - θ}=sin（3π/2）cos θ-cos（3π/2）sinθ=-cosθ