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Tuesday, September 3, 2013

Derivative - Inverse Trigonometric Functions, 3

Category: Differential Calculus, Trigonometry

"Publish in Suisun City, California, USA"

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,


 

Monday, September 2, 2013

Derivative - Inverse Trigonometric Functions, 2

Category: Differential Calculus, Trigonometry

"Published in Suisun City, California, USA"

Prove that


Solution:

Consider the given equation above


Let


Take cosine 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 sin y in the equation. We know that 


but


Hence, the above equation becomes





Finally, the equation becomes



but


Therefore,


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,