InterviewSolution
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InterviewSolution
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Evaluate each of the following:`cot^(-1)1/(sqrt(3))-cos e c^(-1)(-2)+sec^(-1)(2/(sqrt(3)))``cot^(-1){2"cos"(sin^(-1)(sqrt(3))/2)}``cos e c^(-1)(-2/(sqrt(3)))+2cot^(-1)(-1)``tan^(-1)(1/(sqrt(3)))+cot^(-1)(1/(sqrt(3)))+tan^(-1)(sin(-pi/2))` |
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Answer» (i) `cot^-1 (1/sqrt3) - cosec^-1(-2) + sec^-1(2/sqrt3)` `= pi/3 - (-pi/6)+ pi/6= pi/3 + pi/6 + pi/6 = (2pi)/3` (ii) `cot^-1(2cos(sin^-1 (sqrt3/2)))` `= cot^-1 { 2cos(pi/3)}` `= cot^-1{1}= pi/4` (iii) `cosec^-1 (-2/sqrt3) + 2cot^-1(-1)` `= -pi/6 + 2(-pi/4) = - pi/6 + (-pi/2)` `= -(2pi)/3` (iv) `tan^-1(1/sqrt3) + cot^-1(1/sqrt3) + tan^-1(sin(-pi/2))` as `tan^-1 x + cot^-1 x = pi/2` so `pi/2 + tan^-1(-1)` `pi/2 - pi/4 = pi/4` Answers |
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