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`

Explanation

`cot^-1(sqrtcosalpha) - tan^-1(sqrtcosalpha) = x`

`=>tan^-1(1/sqrtcosalpha) - tan^-1(sqrtcosalpha) = x`

`=>tan^-1((1/sqrtcosalpha -sqrtcosalpha)/(1+1/sqrtcosalpha*sqrtcosalpha)) = x`

`=>tan^-1((1-cosalpha)/(2sqrtcosalpha)) = x`

`=>tan x = (1-cosalpha)/(2sqrtcosalpha)`

`=>cotx = 1/tanx = (2sqrtcosalpha)/(1-cosalpha)`

`=>cosecx = sqrt(1+cot^2x) = (1+cosalpha)/(1-cosalpha)`

`=>sinx = 1/(cosecx) = (1-cosalpha)/(1+cosalpha)`

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