已知tana/2=2,a∈(π/2,π)求cosa

Question

已知tan a/2=2,a∈(π/2,π)求cos a

Answer 1

a的范围没有用,
cosa
=cos[2*(a/2)]
=cos²(a/2)-sin²(a/2)
=[cos²(a/2)-sin²(a/2)]/[cos²(a/2)+sin²(a/2)]
分子分母同时除以cos²(a/2)
=[1-tan²(a/2)]/[1+tan²(a/2)]
=(1-4)/(1+4)
=-3/5