Question

tan^2x/1+tan^2x = sin^2x

Answer 1

prove rs=ls

Answer 2

\[\huge \frac{\tan^2{x}}{1+\tan^2{x}}=\frac{\frac{sin^2{x}}{cos^2{x}}}{1+\frac{sin^2{x}}{cos^2{x}}}=\]\[\huge \frac{\sin^2{x}}{\cos^2{x}+\sin^2{x}}=\frac{\sin^2{x}}{1}\]

Answer 3

any way, take 1+tan^2x as sec^2 x
so, left side can be writen :
tan^2x/1+tan^2x = tan^2x/sec^2 x
we knowed that tanx=sinx/cosx and secx = 1/cosx
=> tan^2x/sec^2 x = (sin^2 x/cos^2x)/(1/cos^2 x)
=> tan^2x/sec^2 x = (sin^2 x/cos^2x) * cos^2 x/1 = sin^2 x