Math Help - more problem with identities, what am i doing wrong?

1. more problem with identities, what am i doing wrong?

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

2. Originally Posted by melvis
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

$\sin^2{x}(1 + \cot^2{x}) - 1 = 0$.

$\sin^2{x}\left(1 + \cot^2{x}\right) - 1 = \sin^2{x}\left(1 + \frac{\cos^2{x}}{\sin^2{x}}\right) - 1$

$=\sin^2{x}\left(\frac{\sin^2{x} + \cos^2{x}}{\sin^2{x}}\right) - 1$

$=\sin^2{x}\left(\frac{1}{\sin^2{x}}\right) - 1$

$= 1 - 1$

$= 0$.