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

∵

⇒ Z =

{Using basic limits algebra}

∵ (1- 2sin²x) = cos 2x

As, a² – b² = (a+b)(a-b)

⇒ Z =

Now put the value of x, we have-

∴ Z =

Hence,