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tan^(-1)""(x-y)/(1+xy)+tan^(-1)""(y-z)/(...

`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))`

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

cot^(-1)""(xy+1)/(x-y)+cot^(-1)""(yz+1)/(y-z) +cot ^(-1) "" (zx +1)/(z-x)=0

If tan ^(-1 )""(yz )/( xr ) + tan ^(-1 )""(zx)/(yr) + tan ^(-1) ""(xy)/(zr) =(pi)/(2) , prove that , x^(2) + y^(2) + z^(2) + r^(2)

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

Prove that tan ^(-1)""(1)/(x+y)+ tan ^(-1)""(y)/(x^(2)+xy+1)= cot ^(-1)x.

Find (dy)/(dx) if y=tan^(-1)((4x)/(1+5x^2))+tan^(-1)((2+3x)/(3-2x))

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CHHAYA PUBLICATION-TRIGONOMETRIC INVERSE CIRCULAR FUNCTIONS-Short answer type questions
  1. sin^(-1) ""(2a)/(1+a^(2))-cos^(-1) ""(1-b^(2))/(1+b^(2))=2tan ^(-1) ""...

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  2. cot^(-1)""(xy+1)/(x-y)+cot^(-1)""(yz+1)/(y-z) +cot ^(-1) "" (zx +1)/(...

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

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  4. cos^(-1)x= 2 sin ^(-1) sqrt((1-x)/(2))=2 cos ^(-1)""sqrt((1+x)/(2))=2t...

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  5. { cos (sin ^(-1) x)}^(2) ={sin (cos ^(-1) x)}^(2)

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  6. tan ^(1)(cotx) + cot ^(-1) (tan x)=pi -2x

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  7. tan^(-1) (cot x) +cot^(-1)(tan x) =pi -2x

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  8. sin cos ^(-1) tan (sec^(-1) x) = sqrt(2-x^(2))

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  9. sin "cosec"^(-1) cot (tan^(-1)x) =x

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  10. sin cot^(-1)cos (tan ^(-1)x)=sqrt((x^(2)+1)/(x^(2)+2))(x gt 0)

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  11. tan [(1)/(2) sin^(-1)""(2x)/(1+x^(2))+(1)/(2) cos ^(-1)""(1-y^(2))/(1...

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

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  13. 2 tan ^(-1)""(1+x)/(1-x)+sin ^(-1)""(1-x^(2))/(1+x^(2))

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

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

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

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

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

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

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

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