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

Prove that `tan^(-1)x+tan^(-1)""(2x)/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3x^(2)))absxlt(1)/(sqrt(3)).`

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SURA PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE 4.5
  1. Find the value, it exists. If not give the reson for non-existence. ...

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  2. Find the value, it exists. If not give the reson for non-existence. ...

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  3. Find the value, it exists. If not give the reson for non-existence. ...

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  4. Find the value of the expression in terms of x, with the help of a ref...

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  5. Find the value of the expression in terms of x, with the help of a ref...

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  6. Find the value of the expression in terms of x, with the help of a ref...

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

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  8. Find the value of cot(sin^(-1)""(3)/(5)+sin^(-1)""(4)/(5))

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  9. Find the value of tan (sin^(-1)""(3)/(5)+cot^(-1)""(3)/(2))

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  10. Prove thate tan^(-1)((2)/(11))+tan^(-1)((7)/(24))=tan^(-1)((1)/(2))

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  11. Prove thate sin^(-1)((3)/(5))-cos^(-1)((12)/(13))=sin^(-1)((16)/(65)...

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  12. Prove that tan^(-1)x+tan^(-1)y+tan^(-1)z=tan^(-1)((x+y+z-xyz)/(1-xy-yz...

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  13. If tan^(-1)x+tan^(-1)y+tan^(-1)z=pi, show that x + y + z = xyz.

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  14. Prove that tan^(-1)x+tan^(-1)""(2x)/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3...

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  15. Simplify : tan^(-1)((x)/(y))-tan^(-1)((x-y)/(x+y)).

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  16. Solve sin^(-1)((5)/(x))+sin^(-1)((12)/(x))=(pi)/(2)

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  17. Solve 2tan^(-1)x=cos^(-1)""(1-a^(2))/(1+a^(2))-cos^(-1)""(1-b^(2))/(...

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  18. Solve 2tan^(-1)(cosx)=tan^(-1)(2cosecx)

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  19. Solve cot^(-1)x-cot^(-1)(x+2)=(pi)/(2),xgt0

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  20. Find the number of solution of the eqution tan^(-1)(x-1)+tan^(-1)x+tan...

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