Trouble with Limit of cot^2(x)/(1-csc(x))

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For some reason, I'm having trouble with the following:

limit as x-->pi/2 (cot^2(x))/(1-csc(x))

Any help would be appreciated!
 
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BrownianMan said:
For some reason, I'm having trouble with the following:

limit as x-->pi/2 (cot^2(x))/(1-csc(x))

Any help would be appreciated!

I would multiply by 1 + csc(x) over itself. Keep in mind the identity that involved cot^2(x) and csc^2(x).
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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