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Sunday, September 1, 2013

Derivative - Inverse Trigonometric Functions

Category: Differential Calculus, Trigonometry

"Published in Suisun City, California, USA"

Prove that


Solution:

Consider the above equation


Let


Take sine 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 cos y in the equation. We know that 


but


Hence, the above equation becomes





Finally, the equation becomes



but


Therefore,