trigonometry - Prove or disprove $frac{sqrt{1+tan x}}{cot x} = frac{1+sin x}{cos x}$

I have tried to prove the identity

$$\begin{equation} \frac{\sqrt{1+\tan x}}{\cot x} = \frac{1+\sin x}{\cos x} \end{equation}$$

by $t$-substitution but seem not to work. Please don't solve(don`t post the answer on this site) this question for me just try it and give me hints on how I should go about it. Or if you like you can post but I wanted to try using some hints that you would give first.

Answer

If $x=\pi/4$ we have:

$$\frac{\sqrt{1+1}}{1}=\sqrt{2}$$ on the left, but $$\frac{1+ \frac{1}{\sqrt{2}}}{1/\sqrt{2}}=\sqrt{2}+1$$ on the right.

These are not equivalent.