If `u=cot^-1 sqrt(tanalpha)-tan^-1 sqrt(tan alpha),` then `tan(pi/4-u/2)` is equal to (a) `sqrt(tan alpha)` (b) `sqrt(cos alpha)` (c) `tan alpha` (d) `cot alpha`

Explanation

We have given

`u=cot^-1 sqrt(tanalpha)-tan^-1 sqrt(tan alpha)`

And as we know that

`tan^(−1)alpha+cot^(−1)alpha=(pi)/2`

`u=(pi)/2-2tan^(−1)(sqrttanalpha)`

`2tan^(−1)(sqrttanalpha)=(pi)/2-u`

`tan^(−1)(sqrttanalpha)=(pi)/4-u/2`

`(sqrttanalpha)=tan((pi)/4-u/2)`

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