Derivative - Inverse Trigonometric Functions, 6

Category: Differential Calculus, Trigonometry

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Prove that

Solution:

Consider the given equation above

Let

Take cotangent 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 csc² y in the equation. We know that 

  
but

Hence, the above equation becomes 

Finally, the equation becomes  

but

Therefore,