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The number of real values of x satisfying `tan^-1(x/(1-x^2))+tan^-1 (1/x^3)` is |
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Answer» Correct Answer - no solution Given equation is `tan^(-1) ((x)/(1 -x^(2))) + tan^(-1) ((1)/(x^(3))) = (3pi)/(4)` Clearly `x != +- 1` `tan^(-1) ((x)/(1 - x^(2))) + tan^(-1) ((1)/(x^(3))) = tan.((x)/(1 - x^(2)) + (1)/(x^(3)))/(1 - (x)/(x^(3) (1 - x^(2))))` `= tan^(-1).(x^(4) + 1 -x^(2))/((x^(2) -x^(4) -1) x)` `= tan^(-1).(-(1)/(x))` `:. tan^(-1) (-(1)/(x)) = (3pi)/(4)` `rArr x = 1, " but " x != 1` So the given equation has no solution |
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