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

Prove that `pi/2 le sin ^(-1) x +2 cos^(-1) x lt (3 pi)/(2)`

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PREMIERS PUBLISHERS-INVERSE TRIGONOMETRIC FUNCTIONS -PROBLEMS FOR PRACTICE ( ANSWER THE FOLLOWING QUESTIONS ):
  1. Find the principal value of cos^(-1) cos ((-pi)/4)

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  2. Find the principal value of cos^(-1)cos ((7pi)/6)

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  3. Find the principal value of tan^(-1)((-1)/(sqrt(3)))

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  4. Find the principal value of tan^(-1)tan ((3pi)/4)

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  5. Find the principal value of tan^(-1) (-1)

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  6. Find the domain sin^(-1) (3 - 4x^(2))

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  7. Find the value of sin^(-1) (sin . (5pi)/8 cos . (pi)/8 - cos . (5pi...

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  8. Find the value of cos^(-1)(cos . (5pi)/9 cos .pi/9 - sin . (5pi)/9 ...

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  9. Find the domain of cos^(-1) ((3+sinx)/4)

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  10. Find the value of 2 cos^(-1). (sqrt(3))/2 + sin^(-1). (sqrt(3))/2

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  11. Evaluate : cos^(-1) cos ((6pi)/5) +cos^(-1) cos ((4pi)/3)

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  12. Simplify : tan^(-1)(1) - cos^(-1) ((-1)/2) +sin^(-1) ((-sqrt(3))/2)

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  13. Prove that tan (sin^(-1)x) = x/(sqrt(1-x^(2))) - 1 lt x lt 1 .

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  14. Find the range of tan^(-1)((2x)/(1+x^2))

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  15. Find the derivatives of the following : cos^(-1)((1-x^(2))/(1+x^(2))...

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  16. Prove the following : cos^(-1)((1-x^(2))/(1+x^(2)))=sin^(-1) ((2x)/(...

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  17. Prove that pi/2 le sin ^(-1) x +2 cos^(-1) x lt (3 pi)/(2)

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  18. Show that sin^(-1) (5/13) +cot^(-1) (12/5)= sin^(-1)((120)/169)

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  19. Find the value of tan [ 1/2 "cosec"^(-1) ((1+x^(2))/(2x)) +1/2 sec^...

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  20. y = tan^(-1)((3x-x^(3))/(1-3x^(2))), find dy/dx.

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