The value of x satisfying the equation `cos^(-1)3x+sin^(-1)2x=pi` isA. `x=(1)/(sqrt(3))`B. `x=(-1)/(sqrt(3))`C. `x=(-1)/(sqrt(3))`D. none of these

The value of x satisfying the equation `cos^(-1)3x+sin^(-1)2x=pi` isA.

1.	The value of x satisfying the equation `cos^(-1)3x+sin^(-1)2x=pi` isA. `x=(1)/(sqrt(3))`B. `x=(-1)/(sqrt(3))`C. `x=(-1)/(sqrt(3))`D. none of these
Answer» Correct Answer - D `sin^(-1)2x=pi-cos^(-1)3x` `rArr sin^(-1)2x=cos^(-1)(-3x)` `rArr sqrt(1-4x^(2))=-3x(xlt 0)` `rArr x^(2)=(1)/(13)` `rArr x=(-1)/(sqrt(13))` But for `x lt 0, pi//2 lt cos^(-1)3x lt pi` and `-pi//2 lt sin^(-1)2x lt 0` `therefore L.H.S. ne pi` Hence, equation has no solution.

`tan^(-1)[(cosx)/(1+sinx)]`is equal to`pi/4-x/2,forx in (-pi/2,(3pi)/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-(3pi)/2,pi/2)`
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