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

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

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Verified by Experts

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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