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Prove that cot (cos^(-1) x) = x/(sqr...

Prove that
`cot (cos^(-1) x) = x/(sqrt(1-x^(2))) |x| lt 1 `

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The correct Answer is:
`x/(sqrt(1-x^(2)))`
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PREMIERS PUBLISHERS-INVERSE TRIGONOMETRIC FUNCTIONS -PROBLEMS FOR PRACTICE ( ANSWER THE FOLLOWING QUESTIONS ):
  1. Prove that cot (cos^(-1) x) = x/(sqrt(1-x^(2))) |x| lt 1

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  2. Find the principal value of sin^(-1)"" (1)/(sqrt(2))

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  3. Find the principal value of sin^(-1) (sin (-pi/6))

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  4. Find the principal value of sin^(1) (sin ((6pi)/7))

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  5. Find the principal values of cos^(-1)""(1)/(2)

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  6. Find the principal value of cos^(-1) cos ((-pi)/4)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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