Sin ^ 2 ( 1 + cot ^ 2) - 1 = 0
so I tried to solve like this
(1-cot^2)(1+cot^2) -1
1+cot^ 4 - 1
cot^ 4
What you have said at the moment is meaningless.
I assume you mean that you are trying to prove
$\displaystyle \sin^2{x}(1 + \cot^2{x}) - 1 = 0$.
$\displaystyle \sin^2{x}\left(1 + \cot^2{x}\right) - 1 = \sin^2{x}\left(1 + \frac{\cos^2{x}}{\sin^2{x}}\right) - 1$
$\displaystyle =\sin^2{x}\left(\frac{\sin^2{x} + \cos^2{x}}{\sin^2{x}}\right) - 1$
$\displaystyle =\sin^2{x}\left(\frac{1}{\sin^2{x}}\right) - 1$
$\displaystyle = 1 - 1$
$\displaystyle = 0$.