Derivative - Inverse Trigonometric Functions, 6

Category: Differential Calculus, Trigonometry

"Published in Suisun City, California, USA"

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,

 

Derivative - Inverse Trigonometric Functions, 5

Category: Differential Calculus, Trigonometry

"Published in Newark, California, USA"

Prove that

Solution:

Consider the given equation above

Let

Take cosecant 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 csc y cot y in the equation. We know that

but

Hence, the above equation becomes 

Finally, the equation becomes  

but

Therefore,

 

Derivative - Inverse Trigonometric Functions, 4

Category: Differential Calculus, Trigonometry

"Published in Newark, California, USA"

Prove that

Solution:

Consider the given equation above

Let

Take secant 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 sec y tan y in the equation. We know that  

but

Hence, the above equation becomes 

Finally, the equation becomes 

but

Therefore,