Evaluate the following limits:

As we need to find


We can directly find the limiting value of a function by putting the value of the variable at which the limiting value is asked if it does not take any indeterminate form (0/0 or ∞/∞ or ∞-∞, .. etc.)


Let Z =


we need to take steps to remove this form so that we can get a finite value.


Note: While modifying be careful that you don’t introduce any zero terms in the denominator


As


cosec2x – 1 = cot2x



As, a2 – b2 = (a+b)(a-b)


Thus,




Hence,



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