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Find the value of tan { 1/2 sin^(-1) ...

Find the value of
`tan { 1/2 sin^(-1) ((2x)/(1+x^(2))) + 1/2 cos^(-1) ((1-y^(2))/(1+ y^(2)))}`

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Verified by Experts

The correct Answer is:
`(x+y)/(1-xy)`
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MODERN PUBLICATION-INVERSE - TRIGONOMETRIC FUNCTIONS-EXERCISE 2 (b) (Short Answer Type Questions)
  1. Find the value of tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y))

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  2. Prove that: cot^(-1)((ab+1)/(a-b))+cot^(-1)((bc+1)/(b-c))+cot^(-1)((ca...

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  3. Find the value of tan { 1/2 sin^(-1) ((2x)/(1+x^(2))) + 1/2 cos^(-1...

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  4. Prove that tan[pi/4+1/2cos^(-1)""a/b]+tan[pi/4-1/2cos^(-1)""a/b]=2b/a

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  5. Solve tan^(-1)2x+tan^(-1)3x=pi/4.

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  6. Solve tan^(-1) ((x+1)/(x-1)) + tan^(-1) ((x-1)/x) = tan^(-1)(-7)

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  7. Solve : tan^(-1)(x-1)/(x-2)+tan^(-1)(x+1)/(x+2)=pi/4

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  8. Solve sin^(-1) (1 - x) - 2 sin^(-1) x = (pi)/(2)

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  9. Solve for x : 2tan^(-1)(sinx)=tan^(-1)(2secx),\ x!=pi/2

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  10. Solve : 2 tan^(-1), (cos x) = tan^(-1), (2 cosec x)

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  11. Solve the following equations : tan^(-1) (x+2) +tan^(-1) (x-2) = ta...

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  12. Solve the following equations : tan^(-1) (x+1) +tan^(-1) (x-1) = ...

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

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  14. If tan ^(-1) ((1-x)/(1+x))= (1)/(2) tan^(-1) x, x gt 0, then x = ?

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  15. Solve the following equations : tan^(-1). (2x)/(1-x^(2)) +cos^(-1)....

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  16. Solve the following equations : cos (tan^(-1) x ) = sin (cot^(-1)...

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  17. If sin(cot^(-1)(x+1))=costan^(-1)x, then x=

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  18. Solve the following equations : 2tan^(-1) (sin x) = tan^(-1) (2se...

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  19. Solve the following equations : cos (sin^(-1) x) = 1/2

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  20. Solve the following equations : tan^(-1) ((x-2)/(x-4)) +tan^(-1) (...

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