If `cot^(-1)(sqrt(cosalpha))-tan^(-1)(sqrt(cosalpha))=x ,` then `sinx` is `tan^2alpha/2` (b) `cot^2alpha/2` (c) `tan^2alpha` (d) `cotalpha/2`

Options

A. `sqrt(tan alpha)`
B. `sqrt(cot alpha)`
C. `tan alpha`
D. `cot alpha`

Answer

A

Explanation

Let `sqrt(tan alpha) = tan x`. Then
`u = cot^(-1) (tan x) - tan^(-1) (tan x)`
`= (pi)/(2) - x -x = (pi)/(2) - 2x`
or `2x = (pi)/(2) -u`
or `x = (pi)/(4) - (u)/(2)`
or `tan x = tan ((pi)/(4) -(u)/(2))`
`rArr sqrt(tan alpha) = tan ((pi)/(4) - (u)/(2))`