InterviewSolution
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InterviewSolution
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If `-1 lt x lt 0`, then `cos^(-1) x` is equal toA. `sec^(-1).(1)/(x)`B. `pi - sin^(-1) sqrt(1 -x^(2))`C. `pi + tan^(-1).(sqrt(1 -x^(2)))/(x)`D. `cot^(-1).(x)/(sqrt(1 -x^(2)))` |
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Answer» Correct Answer - A::B::C::D `cos^(-1) x = sec^(-1).(1)(x) " for all " x in [-1, 0)` Leet `x = -y` `:. Cos^(-1) x = cos^(-1) (-y) = pi - cos^(-1) y` `= pi - sin^(-1) sqrt(1 -y^(2))`...(i) `=pi - tan^(-1).(sqrt(1 - y^(2)))/(y)` ..(ii) From (i), `cos^(-1) = pi - sin^(-1) sqrt(1 - y^(2)) = pi - sin^(-1) sqrt(1 -x^(2))` From (ii), `cos^(-1) x = pi - tan^(-1).(sqrt(1 -y^(2)))/(y)` `= pi - tan^(-1).(sqrt(1 -x^(2)))/(-x)` `= pi + tan^(-1).(sqrt(1 -x^(2)))/(x)` `= pi + cot^(-1).(x)/(sqrt(1 -x^(2))) -pi " " ("as " x lt 0)` `= cot^(-1).(x)/(sqrt(1 -x^(2)))` |
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