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

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SUMMARY

The limit as x approaches π/2 of the expression (cot²(x))/(1-csc(x)) can be resolved by multiplying the numerator and denominator by (1 + csc(x)). This technique utilizes the identity cot²(x) = csc²(x) - 1, which simplifies the limit evaluation. The final result confirms that applying trigonometric identities is essential for solving limits involving cotangent and cosecant functions.

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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).
 

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