Choose the correct answer

If then, =

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,

Or,

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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