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`x=(1)/(sqrt(3))``x=(-1)/(sqrt(3))``x=(-1)/(sqrt(3))`none of these

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`sin^(-1)2x=pi-cos^(-1)3x` <br> `rArr sin^(-1)2x=cos^(-1)(-3x)` <br> `rArr sqrt(1-4x^(2))=-3x(xlt 0)` <br> `rArr x^(2)=(1)/(13)` <br> `rArr x=(-1)/(sqrt(13))` <br> But for `x lt 0, pi//2 lt cos^(-1)3x lt pi` and `-pi//2 lt sin^(-1)2x lt 0` <br> `therefore L.H.S. ne pi` <br> Hence, equation has no solution. **Definition and geometric meaning.**

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