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Evaluate
Solution:
To get the value of a given function, let's substitute the value of x to the above equation, we have
Since the answer is 0/0, then it is an Indeterminate Form which is not accepted as a final answer in Mathematics. We have to do something first in the given equation so that the final answer will be a real number, rational, or irrational number.
Method 1:
Since the answer is Indeterminate Form, then we have to use the principles of trigonometric identities. Let's convert the double angle function into single angle function and then simplify as follows
Substitute the value of x to the above equation, we have
Therefore,
Method 2:
Another method of solving Indeterminate Form is by using L'Hopital's Rule. This is the better method especially if the rational functions cannot be factored. L'Hopitals Rule is applicable if the Indeterminate Form is either 0/0 or ∞/∞. Let's apply the L'Hopital's Rule to the given function by taking the derivative of numerator and denominator with respect to x as follows
Substitute the value of x to the above equation, we have
Therefore,
