Simplify the expression: $\sin x (1+\cot^2 x)$ Simplify the expression: $\sin x (1+\cot^2 x)$


Please help. I have tried all identities and still can't figure it out. Thanks.
Note the following identity:
$$\sin^2{x}+\cos^2{x}\equiv 1$$
If you divide both sides by $\sin^2{x}$, you can derive another identity:
$$1+\cot^2{x}\equiv \csc^2{x}$$
Can you continue?
I assume you mean the expression

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

However, it's not becoming much simpler. There are many forms that you can give for this expression. Ask Wolfram Alpha for more expressions. According to Wolfram, it can also be $\csc(x)$.