InterviewSolution
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InterviewSolution
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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` |
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Answer» `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)` `=>sinx = sin^2(alpha/2)/cos^2(alpha/2) = tan^2(alpha/2)` So, option `(a)` is the correct option. |
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