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Prove that sin(2 tan^-1(sqrt((1+x)/(1-...

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

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PRADEEP PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. Prove that 2 tan^-1 (1/x) = sin^-1 ((2x)/(1+x^2)), |x| ge 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Express the following functions in the simplest form : tan^-1 (a cos...

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  17. Solve : cot^-1(2x)+cot^-1(3x)=pi/4

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  18. Solve the following equations. cot^-1 x - cot^-1 (x+2) = pi/12, x > ...

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  19. Solve the following equations: tan^-1((1-x)/(1+x)) = 1/2 tan^-1 x, x...

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  20. Solve the 2 tan^-1 (cos x) = tan^-1 (2 cosec x).

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