Like for an example:
Prove:
sin(x) + cos(x)cot(x) = csc(x)
And more complex problems like:
(tan^2(x) / (sec(x) + 1)) = (1-cos(x)) / cos(x)
Is there a special technique to follow?
In establishing an identity, its best that you work with the side of the equation that seems to be more complex.
In the first one, I'd focus on getting the left side of the equation to look like the right side of the equation:
$\displaystyle \sin x+\cos x\cot x=\sin x+\cos x\frac{\cos x}{\sin x}=\sin x+\frac{\cos^2 x}{\sin x}$
Now, find the LCD, and then combine the fractions:
LCD = $\displaystyle \sin x$
$\displaystyle \therefore\sin x+\frac{\cos^2 x}{\sin x}=\frac{\sin^2x}{\sin x}+\frac{\cos^2x}{\sin x}=\frac{\overbrace{\sin^2x+\cos^2x}^1}{\sin x}=\frac{1}{\sin x}=\color{red}\boxed{\csc x}$
We've established that the LHS = RHS.
Can you try the other one?
I would focus on getting the LHS to look like the RHS...
Does this make sense?
--Chris