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,



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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