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If 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-...

If `3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x)/(1-x^2))=pi/3,` then `x` is equal to (A) `1/(sqrt(3))` (B) `-1/(sqrt(3))` (C) `sqrt(3)` (D) - `(sqrt(3))/4`

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Given, `3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x)/(1-x^2))=pi/3,`
`2tan^(−1)x=tan^(−1)[(2x)/(1-x^2)​]=sin^(−1)[(2x)/(1+x^2)​]=cos^(−1)[(1−x^2)/(1+x^2)​]`
= `3(2tan^(-1))(x)-4(2tan^(-1)x)+2(2tan^(-1)x)=pi/3,`
=`2tan^(-1)x=pi/3`
=`x=tan(pi/6)`
=`x=1/sqrt(3)`
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
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  14. Find the principal values of sin^(-1)(1/2)

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