Derivative - Inverse Trigonometric Functions, 3

Category: Differential Calculus, Trigonometry

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Prove that

Solution:

Consider the given equation above

Let

Take tangent on both sides of the equation, we have

Take the derivative on both sides of the equation with respect to x, we have 

Next, we need to eliminate sec² y in the equation. We know that  

but

Hence, the above equation becomes

Finally, the equation becomes

but

Therefore,