Choose the correct answer
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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