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If tan^-1(1/y)=-pi+cot^-1 y, where y=x^2...

If `tan^-1(1/y)=-pi+cot^-1 y,` where `y=x^2-3x+2,` then find the value of `x`

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The correct Answer is:
`x in (1, 2)`
`tan^(-1) ((1)/(y)) = -pi + cot^(-1) y`
`rArr y lt 0`
`rArr x^(2) - 3x + 2 lt 0`
`rArr (x - 1) (x -2) lt 0`
`rArr x in (1, 2)`
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CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
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  3. If tan^-1(1/y)=-pi+cot^-1 y, where y=x^2-3x+2, then find the value of ...

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  4. If sin^-1x+sin^-1y=(2pi)/3, then cos^-1x+cos^-1y=

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  5. solve the equation cot^-1 x + tan^-1 3 = pi/2

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  6. Solve 2 cos^(-1) x + sin^(-1) x = (2pi)/(3)

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  7. Prove that sin^(-1) cos (sin^(-1) x) + cos^(-1) x = (pi)/(2), |x| le 1

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  8. If sin^(-1)x+sin^(-1)y=(2pi)/3 and cos^(-1)x-cos^(-1)y=-pi/3 then the ...

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

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

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

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

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

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

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

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

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

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

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