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If cos^(-1)(6x)/(1+9x^2)=-pi/2+tan^(-1)3...

If `cos^(-1)(6x)/(1+9x^2)=-pi/2+tan^(-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-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. sin{2cos^(-1)((-3)/(5))}=

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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+tan^(-1)3x , then find the value ofxdot

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  4. Find the value of 2cos^(-1)3/(sqrt(13))+cot^(-1)(16)/(63)+1/2cos^(-1)7...

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

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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 -1

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

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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 + tan^(-1). (sqrt(1 - x^(2)...

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

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  17. Find the value of tan^(-1) (-tan.(13pi)/(8)) + cot^(-1) (-cot((19pi)/(...

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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 sin^(-1) (sin 5) gt x^(2) - 4x

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