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Solve tan^(-1) x gt cot^(-1) x...

Solve `tan^(-1) x gt cot^(-1) x`

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Verified by Experts

The correct Answer is:
`x gt 1`
`tan^(-1) x gt cot^(-1) x`
`rArr tan^(-1) x gt pi//2 - tan^(-1) x`
`rArr tan^(-1) x gt pi//4`
`rArr x gt 1`
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CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Show that sin^-1 x+cos^-1 x=pi/2.

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  2. If (tan^(-1) x)^2 + (cot^(-1) x)^2 = (5 pi^2) /8 find x.

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  3. Solve tan^(-1) x gt cot^(-1) x

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  4. If alpha is the only real root of the equation x^3 + bx^2 + cx + 1 = ...

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  5. If alpha in (-(pi)/(2), 0), then find the value of tan^(-1) (cot alpha...

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  6. Find the maximum value of (sec^(-1) x) (cosec^(-1) x), x ge 1

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  7. Solution of the equation sin (sqrt(1+sin 2 theta))= sin theta + cos th...

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  8. Prove that tan^(-1).(1)/(sqrt2) + sin^(-1).(1)/(sqrt5) - cos^(-1).(1)/...

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  9. Solve : tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=(pi)/(4)

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  10. The number of real values of x satisfying tan^-1(x/(1-x^2))+tan^-1 (1...

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  11. Prove : 2 sin ^(-1) "" 3/5 = tan ^(-1) ""(24)/(7)

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  12. Find (dy)/(dx) in the following : y = tan^(-1)((3x-x^(3))/(1-3x^(2))...

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  13. Solve : 2 tan^(-1) (cos x ) = tan^(-1) (2 "cosec" x)

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  14. Solve the tan^(-1)((1-x)/(1+x))=(1)/(2)tan^(-1)x for x gt0.

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  15. If x + y + z = xyz and x, y, z gt 0, then find the value of tan^(-1) x...

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  16. If alpha and beta (alpha gt beta) are the roots of x^(2) + kx - 1 =0, ...

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  17. Find the sum cot^(-1) 2 + cot^(-1) 8 + cot^(-1) 18 + ...oo

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  18. Prove that sum(r=1)^(n) tan^(-1) ((2^(r -1))/(1 + 2^(2r -1))) = tan^(...

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  19. If cos^(-1).(x)/(2) + cos^(-1).(y).(3) = (pi)/(6), then prove that (x^...

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  20. Find the set of value of x for which the equation cos^(-1) x + cos^(-1...

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