Answer :

We are given with

u = cot-1{√tan θ} – tan-1{√tan θ}

We need to find the value of .

Let √tan θ = x

Then, u = cot-1{√tan θ} – tan-1{√tan θ} can be written as

u = cot-1 x – tan-1 x …(i)

We know by the property of inverse trigonometry,


Substituting the value of cot-1 x in equation (i), we get

u = (cot-1 x) – tan-1 x

Rearranging the equation,

Now, divide by 2 on both sides of the equation.

Taking tangent on both sides, we get

Using property of inverse trigonometry,

tan(tan-1 x) = x

Recall the value of x. That is, x = √tan θ

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