Question

证明：(2sinX-sin2X)/(2sinX+sin2X)=tan^2X/2

Answer 1

(2sinX-sin2X)/(2sinX+sin2X)

=(2-2cosx)/(2+2cosx)

=(1-cosx)/(1+cosx);

tan^2(x/2)

=sin^2(x/2)/cos^2(x/2)

=[(1-cosx)/2]/[(1+cosx)/2]

=(1-cosx)/(1+cosx);

得证.