InterviewSolution
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InterviewSolution
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Solve `tan^(-1) x + sin^(-1) x = tan^(-1) 2x` |
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Answer» `tan^(-1) x + sin^(-1) x = tan^(-1) 2x` `rArr sin^(-1) x = tan^(-1) 2x - tan^(-1) x` `rArr tan^(-1).(x)/(sqrt(1 - x^(2))) = tan^(-1) [(2 x - x)/(1 + 2x^(2))]` `rArr (x)/(sqrt(1 - x^(2))) = (x)/(1 + 2x^(2))` `rArr 2x^(3) + x = x sqrt(1 - x^(2))` `rArr 2x^(3) - x sqrt(1 - x^(2)) + x = 0` `rArr x(2x^(2) - sqrt(1 - x^(2)) + 1) = 0` `rArr x = 0 " or " 2x^(2) + 1 = sqrt(1 - x^(2))` `rArr x = 0 " or " 4x^(4) + 4x^(2) + 1 = 1 - x^(2)` `rArr x = 0 " or " 4x^(4) + 5x^(2) = 0` `rArr x = 0` is the only solution |
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