Question

求证明高中数学三角公式证明求证：tan(a/2)=sina/(1+cosa)=(1-cosa)/sina

Answer 1

证明:

sina/(1+cosa)

=2sin(a/2)cos(a/2)/(1+2cos²(a/2)-1)

=2sin(a/2)cos(a/2)/(2cos²(a/2))

=sin(a/2)/cos(a/2)

=tan(a/2)

(1-cosa)/sina

=[1-(1-2sin²(a/2))]/[2sin(a/2)cos(a/2)]

=2sin²(a/2)/[2sin(a/2)cos(a/2)]

=sin(a/2)/cos(a/2)

=tan(a/2)

∴tan(a/2)=sina/(1+cosa)=(1-cosa)/sina