If Y = Tan^1x Prove That Yn = (-1)^(n-1)! Sin n(𝞹/2 - y) Sin^n (𝞹/2 - y) - Math Traders

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If Y = Tan^1x Prove That Yn = (-1)^(n-1)! Sin n(𝞹/2 - y) Sin^n (𝞹/2 - y)

 Y = Tan^1x Prove That Yn = (-1)^(n-1)! Sin n(𝞹/2 - y) Sin^n (𝞹/2 - y)

In This math tutorial we will see that if  Y = Tan^1x or tan inverse x then we have to prove that 

Yn = (-1)^(n-1)! Sin n(𝞹/2 - y) Sin^n (𝞹/2 - y)

we will solve this question with successive differentiation method to find nth derivatives of  Y = Tan^1x and to prove Yn = (-1)^(n-1)! Sin n(𝞹/2 - y) Sin^n (𝞹/2 - y).

A complete solution is given below:

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Nth Derivative - Y = Tan^1x Prove That Yn = (-1)^(n-1)! Sin n(𝞹/2 - y) Sin^n (𝞹/2 - y)

Nth Derivative - Y = Tan^1x Prove That Yn = (-1)^(n-1)! Sin n(𝞹/2 - y) Sin^n (𝞹/2 - y)

Nth Derivative - Y = Tan^1x Prove That Yn = (-1)^(n-1)! Sin n(𝞹/2 - y) Sin^n (𝞹/2 - y)

Nth Derivative - Y = Tan^1x Prove That Yn = (-1)^(n-1)! Sin n(𝞹/2 - y) Sin^n (𝞹/2 - y)

Nth Derivative - Y = Tan^1x Prove That Yn = (-1)^(n-1)! Sin n(𝞹/2 - y) Sin^n (𝞹/2 - y)


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