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Prove that tan^-1 sqrtx = sin^-1 sqrt(...

Prove that
`tan^-1 sqrtx = sin^-1 sqrt(x/1+x) = 1/2cos^-1 ((1-x)/(1+x)), x ge 0`

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Prove that : tan^-1 x +tan^-1 2x/(1-x^2) = tan^-1 ((3x-x^3)/(1-3x^2)), |x| < 1/sqrt3

Prove that tan(sec^-1 x) = sqrt(x^2 - 1) for x le 1

Prove that 2 tan^-1 (1/x) = sin^-1 ((2x)/(1+x^2)), |x| ge 1

Prove that cot^-1 x = cosec^-1 sqrt(1+x^2) for x ge 0

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PRADEEP PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. Prove that tan^-1(1+x)/(1-x) = pi/4 + tan^-1x, x < 1

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  2. Prove that 3 tan^-1 x = tan^-1(3x-x^3)/(1-3x^2), |x| < 1/sqrt3

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  3. Prove that tan^-1 sqrtx = sin^-1 sqrt(x/1+x) = 1/2cos^-1 ((1-x)/(1+x...

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  4. Prove that tan^-1((sqrtx + sqrty)/(1 - (sqrtxy)) = tan^-1 sqrt x + t...

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  5. Prove that tan^-1 (x+sqrtx)/(1-xsqrtx) = tan^-1 x + tan^-1 sqrtx, 0 ...

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  6. Prove that 2 tan^-1 (1/x) = sin^-1 ((2x)/(1+x^2)), |x| ge 1

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  7. Prove that sec (tan^-1( x/2)) = sqrt(4+x^2)/2

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  8. Prove that sin(2 tan^-1(sqrt((1+x)/(1-x))) = sqrt(1-x^2) , - le x < ...

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  9. tan^(-1) sqrt(x) = (1)/(2) cos^(-1) ((1-x)/(1+x)), x in [0, 1]

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  10. Prove that cos(2 tan^-1 (sqrt((1-x)/(1+x)))) = x, - 1 < x le 1

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  11. Prove that : tan^-1((6x-8x^3)/(1-12x^2))- tan^-1(4x/(1-4x^2)) = tan^-1...

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  12. Write in the simplest form : tan^-1 (sin x/(1 + cos x))

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  13. Write in simplest form : "tan"^(-1)(sqrt((1-"cos"x)/(1+"cos"x))),xltpi...

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  14. Write the following in the simplest form tan^(-1)((cosx+sinx)/(cosx-...

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  15. Express the following functions in the simplest form : tan^-1(x/(sqr...

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  16. Express the following functions in the simplest form : tan^-1((2sqrt...

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  17. Express the following functions in the simplest form : tan^-1 (sqrt(...

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  18. Express the following functions in the simplest form : cot^-1(sqrt(1...

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  19. Express the following functions in the simplest form : tan^-1(3x - x...

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  20. Express the following functions in the simplest form : tan^-1 ((3a^2...

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