Question

if,f(x)=1-x/1+x,then prove that f(cosx)=tan²x/2

Answer 1

put x=cos X
f(cosx)=(1-cosx) /(1+cos x)
=(1-(cos^2 x/2 -sin^2. x/2))/(1+(cos^2 x/2 - sin ^2 x/2))
=[sin^2. (x/2)] / [cos^2 (x/2).]
=tan^2 (x/2)

Answer 2

1-cosx/1+cosx=2sin
$\frac{1 - cosx}{1 + cosx} = \frac{2sin { \frac{x}{2} }^{2} }{2cos { \frac{x}{2} }^{2} } = tan { \frac{x}{2} }^{2}$
is it ok..