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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`A. `sqrt(tan alpha)`B. `sqrt(cot alpha)`C. `tan alpha`D. `cot alpha` |
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Answer» Correct Answer - A 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))` |
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