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Solve sec^(-1) x gt cosec^(-1) x...

Solve `sec^(-1) x gt cosec^(-1) x`

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The correct Answer is:
`x in (-oo, -1] uu (sqrt2, oo)`
`sec^(-1) x gt pi//2 - sec^(-1) x`
`rArr sec^(-1) x gt pi//4`
`rArr sec^(-1) x in ((pi)/(4), (pi)/(2)) uu ((pi)/(2) , pi]`
`rArr x in (-oo, -1) uu (sqrt2, oo)`
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CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. If sin^(-1)x+sin^(-1)y=(2pi)/3 and cos^(-1)x-cos^(-1)y=-pi/3 then the ...

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

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  3. Solve sec^(-1) x gt cosec^(-1) x

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

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

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

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

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  8. If equation sin^(-1) (4 sin^(2)theta + sin theta) + cos^(-1) (6 sin th...

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  9. Find the value of sin^(-1) ((3)/(5)) + tan^(-1) ((1)/(7))

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  10. If x gt y gt 0, then find the value of tan^(-1).(x)/(y) + tan^(-1) [(x...

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

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

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

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  14. Prove the following: 2\ sin^(-1)(3/5)=tan^(-1)(24/7)

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  15. Write the following function in the simplest form: tan^(-1)((3a^2x-x^3...

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  16. Solve the equation 2 tan^(-1) (cos x) = tan^(-1) (2 cosec x)

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  17. Solve the equations.tan^(-1)((1-x)/(1+x))=1/2tan^(-1)x ,(x >0)

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

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

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

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