If `u=cot^(-1)sqrt(tanalpha)-tan^(-1)sqrt(tanalpha),t h e ntan(pi/4- u/2)i se q u a l` (a)`sqrt(tanalpha)` (b) `sqrt(cotalpha)` (c)`tanalpha` (d) cot `alpha`

Explanation

Let `sqrt (tanalpha) = tanx`

Then, the given equation becomes,

`u= cot^-1(tanx) - tan^-1(tanx)`

`=>u= pi/2-tan^-1(tanx) - tan^-1(tanx)`

`=>u = pi/2-x-x`

`=>u = pi/2-2x`

`=>x = pi/4 - u/2`

`=>tanx = tan(pi/4-u/2)`

...