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

`2 tan ^(-1)""(1+x)/(1-x)+sin ^(-1)""(1-x^(2))/(1+x^(2))`

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The correct Answer is:
`pi`
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show that 2 tan ^(-1) ((1+x)/(1-x)) - cos ^(-1)( (1-x^(2))/(1+x^(2)))=(pi)/(2)

3 sin ^(-1 ) ""(2x )/(1+x^(2))-4cos^(-1) ""(1-x^(2))/(1+x^(2))+2tan ^(-1)""(2x )/(1-x^(2))=(pi)/(3)

tan ^(-1)""(1-x)/(1+x)- tan ^(-1 )""(1-y)/(1+y) = sin ^(-1) ""(y-x)/(sqrt((1+x^(2))(1+y^(2)))

If x_1=2tan^(-1)((1+x)/(1-x)),x_2=sin^(-1)((1-x^2)/(1+x^2)) , where x in (0,1), then x_1+x_2 is equal to (a) 0 (b) 2pi (c) pi (d) none of these

tan (cos ^(-1) x) = sin (cot ^(-1) ""(1)/(2))

tan ^(-1)""(1-x)/(1+x)""=(1)/(2) sin ^(-1)""(x)/(sqrt(1+x^(2)))

If x in (0, 1) , then find the value of tan^(-1) ((1 -x^(2))/(2x)) + cos^(-1) ((1 -x^(2))/(1 + x^(2)))

tan^(-1)""(x-y)/(1+xy)+tan^(-1)""(y-z)/(1+yz)+tan^(-1)""(z-x)/(1+zx) =tan^(-1)""(x^(2)-y^(2))/(1+x^(2)y^(2))+tan^(-1)""(y^(2)-z^(2))/(1+y^(2)z^(2))+tan^(-1) ""(z^(2)-x^(2))/(1+z^(2)x^(2))

If x_(1) = 2 tan^(-1) ((1 + x)/(1 -x)), x_(2) = sin^(-1) ((1 - x^(2))/(1 + x^(2))), " where " x in (0, 1) , then 2( x_(1) + x_(2) ) is equal to

tan((1)/(2) sin ^(-1)""(2x)/(1+x^(2))+(1)/(2)cos^(-1)((1-x^(2))/(1+x^(2))))=(2x)/(1-x^(2))(|x|ne 1)

CHHAYA PUBLICATION-TRIGONOMETRIC INVERSE CIRCULAR FUNCTIONS-Short answer type questions
  1. tan [(1)/(2) sin^(-1)""(2x)/(1+x^(2))+(1)/(2) cos ^(-1)""(1-y^(2))/(1...

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  2. cos (2cos ^(-1) x+sin ^(-1) x) , " when " x=(1)/(5) where 0 le ...

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  3. 2 tan ^(-1)""(1+x)/(1-x)+sin ^(-1)""(1-x^(2))/(1+x^(2))

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  4. tan (sin ^(-1)x+sin ^(-1) y) +tan (cos^(-1)x+cos ^(-1)y)

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  5. If xy=1 + a^(2) then show that tan^(-1) ""(1)/(a+x)+tan ^(-1) ...

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  6. "If " tan^(-1) x+ tan^(-1) y+tan ^(-1)z=(pi)/(2) , show that , x...

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  7. if tan ^(-1) x+tan ^(-1) y+tan ^(-1) z=pi prove that x+y+z=xyz

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  8. if cos^(-1)x+cos ^(-1)y+cos^(-1) z=pi prove that x^(2) +y^(2)+z...

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  9. "if " sin^(-1) x +sin ^(-1) y+sin ^(-1) z=pi show that , x^(4)+y...

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  10. IF cos (alpha +beta )=(5)/(13) and cos (alpha - beta )=(4)/(5), t...

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  11. If tan ^(-1) y= 4 tan ^(-1) x , find the algebric relation bet...

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  12. If tan ^(-1)x , tan ^(-1) y and tan^(-1) z are in A.P find t...

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  13. tan ^(-1) (x+1) + tan^(-1) (x-1) = tan ^(-1)"" (8)/(31)

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  14. tan (cos ^(-1) x) = sin (cot ^(-1) ""(1)/(2))

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  15. tan ^(-1)((1)/(2) sec x) + cot^(-1)(2cos x) =(pi)/(3)

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  16. sin ^(-1) ""(2a)/(1+a^(2))+sin ^(-1) ""(2b)/(1+b^(2) ) = 2 tan ^(-1...

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  17. tan ^(-1) ""(x-1)/(x-2) + tan ^(-1) ""(x+1)/(x+2)=(pi)/(4)

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  18. tan ^(-1) ""(x-1)/(x-2) +tan ^(-1) ""(x+1)/(x+2)=(pi)/(4)

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  19. sin ^(-1)cos sin^(-1)""x=(pi)/(3)

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  20. tan^(-1)x+tan^(-1) (1-x) = 2 tan ^(-1) sqrt(x(1-x))

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