Question

verify sin^2(x/2)= tanx-sinx/2tanx

Answer 1

tan = sin/ cos
sin/cos-sin/(2*sin/cos)=sin/cos - sin*cos/(2 sin)=sin/cos - cos/2
=\[ \frac{ \sin }{ \cos } -\frac{ \cos }{ 2 }\]

Answer 2

\[\frac{ 2\sin-\cos^2 }{ 2*\cos }\]

Answer 3

now remove cos from this using trigo formulas

Answer 4

or sin^2x/2=(1-cosx)/2............we know cos2x=1-2sin^2x
\[\tan ^2x=\frac{ 1-cosx }{ 1+cosx }\]

Answer 5

1-cosx=(1+cosx)*(tan^2x)

Answer 6

sin^2(x/2)=(1-cosx)/2=(1+cosx)*tan^2x/2

Answer 7

1+cosx=2cos^2(x/2)
(2cos^2(x/2)*tan^2(x/2))/2=sin^2(x/2)