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If cos^(-1)((6x)/(1+9x^2))=-pi/2+2tan^(-...

If `cos^(-1)((6x)/(1+9x^2))=-pi/2+2tan^(-1)3x ,` then find the value of`xdot`

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`cos^(-1).(6x)/(1 + 9 x^(2)) = -(pi)/(2) + 2 tan^(-1) 3x`
`(pi)/(2) - sin^(-1).(6x)/(1 + 9x^(2)) = -(pi)/(2) + 2 tan^(-1) 3x`
`sin^(-1).(6x)/(1 + 9x^(2)) = pi - 2 tan^(-1) 3x`
`sin^(-1).(2 xx 3x)/(1 + (3x)^(2)) = pi - 2 tan^(-1) 3x`
It is true when `3x gt 1`
or `x gt (1)/(3)`
i.e., `x in ((1)/(3), oo)`
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CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Prove that sin^(-1)((2x)/(1+x^2))=tan^(-1)((2x)/(1-x^2))

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  2. If sin^(-1)((4x)/(x^2+4))+2tan^(-1)(-x/2) is independent of x , find t...

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  3. If cos^(-1)((6x)/(1+9x^2))=-pi/2+2tan^(-1)3x , then find the value ofx...

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  4. Find the value of 2cos^(-1)(3/(sqrt(13)))+cot^(-1)(16/63)+1/2cos^(-1)(...

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  5. Find the principal value of (a) cosec^(-1) (-1) (b) cot^(-1) (-(1)/(...

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  6. Solves cos^(-1) x lt 2

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  7. Find the possible values of sin^(-1) (1 - x) + cos^(-1) sqrt(x -2)

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  8. Find the real values of x for which the function f(x) = cos^(-1) sqrt(...

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  9. Find the smallest and the largest values of tan^(-1) ((1 - x)/(1 + x))...

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  10. Find the value of x for which sin^(-1) (cos^(-1) x) lt 1 and cos^(-1) ...

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  11. Solve sin^(-1) x gt tan^(-1) x

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  12. Find the range of f(x) = cos^(-1) x + cot^(-1) x

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  13. If (sin^(-1)x)^2+(sin^(-1)y)^2+(sin^(-1)z)^2=3/4pi^2 , find the value ...

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  14. Find the value of sin(1/4)cos^(-1)((-1)/9)

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  15. If x lt 0, then prove that cos^(-1) x = pi - sin^(-1) sqrt(1 - x^(2))

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  16. Prove that sin^(-1). ((x + sqrt(1 - x^(2)))/(sqrt2)) = sin^(-1) x + (p...

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  17. Find the following values : (a) tan^(-1) (tan13pi/5) (b) sec^(-1)( s...

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  18. If f(x) = sin^(-1) (sin ("log"(2) x)), then find the value of f(300)

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  19. find the maximum value of f(x) = (sin^(-1) (sin x))^(2) - sin^(-1) (si...

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  20. Solve for sin^(-1) (sin 5) gt x^(2) - 4x

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