# Find x where 0<=x<=2pi sin x - cot^2 x = 1 Anyone know how to do these things??

May 21, 2018

We can rewrite:

$\sin x = 1 + {\cot}^{2} x$

Now recall that ${\cot}^{2} x + 1 = {\csc}^{2} x$.

$\sin x = {\csc}^{2} x$

$\sin x - \frac{1}{\sin} ^ 2 x = 0$

$\frac{{\sin}^{3} x - 1}{\sin} ^ 2 x = 0$

${\sin}^{3} x = 1$

$\sin x = 1$

$x = \frac{\pi}{2}$

We can confirm graphically our answer is correct.

Hopefully this helps!