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

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

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

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

prove that . Tan ^(-1) x- tan ^(-1 )y = cos ^(-1) (1+xy)/(sqrt((1+x^(2))(1+y^(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))

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

sin^(-1)x+sin^(-1)y=cos^(-1)""{sqrt((1-x^(2))(1-y^(2)))-xy}

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

If y= tan^(-1) ((sqrt(1+x^(2))-1)/x) , then y'(1) =

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

solve : tan^(-1) sqrt(x(x+1))+sin ^(-1) (sqrt(1+x+x^(2)))=(pi)/(2)

CHHAYA PUBLICATION-TRIGONOMETRIC INVERSE CIRCULAR FUNCTIONS-Long answer type questions
  1. tan ( 2 tan ^(-1)sqrt((1+cos theta)/(1-cos theta)))+ tan theta =0

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  2. tan ^(-1) ""{(sqrt(1+cos x)+sqrt(1-cos x)}/{sqrt(1+cosx)-sqrt(1-cos x)...

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  3. cos ^(-1) ""((cos x + cos y)/(1+cos x cos y))= 2 tan ^(-1) (tan ...

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  4. (1)/(2)cos ^(-1)""((5 cos x +3)/(5+3 cos x))= tan^(-1)""((1)/(2)tan "...

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  5. tan ^(-1)""(1-x)/(1+x)- tan ^(-1 )""(1-y)/(1+y) = sin ^(-1) ""(y-x)/(...

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  6. If cos ^(-1) x+ cos ^(-1) y= theta , show that x^(2)-2xycos thet...

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  7. If sin ( pi cos theta ) = cos (pi sin theta ), , then sho...

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  8. Prove that , a cos theta + b sin theta = sqrt(a^(2) +b^(2) ) cos ...

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  9. IF 2 cos 4 theta + 9 cos 2 theta -7=0 , then show that , theta ...

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  10. cot ^(-1)""x+cot^(-1)""2x=(3pi)/(4)

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  11. cot ^(-1)x+cot^(-1)(a^(2)-x+1)=cot ^(-1)(a-1)

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

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  13. sin ^(-1) x+sin ^(-1) (1-x) = cos ^(-1) x

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  14. cos^(-1) ""(5)/(x)+cos^(-1) ""(12)/(x)=(pi)/(2)

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  15. 3 cot ^(-1)""(1)/(2-sqrt(3))+cot ^(-1)""x=(pi)/(2)

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  16. sin^(-1)x+sin ^(-1)""2x=(pi)/(3)

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  17. sin ^(-1)sqrt(3)x+sin ^(-1)x=(pi)/(2)

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  18. sin^(-1)x-sin ^(-1)y=(pi)/(3) and cos^(-1) x+ cos ^(-1) y=(2pi)/(3)

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  19. sin ^(-1)""(ax)/(C ) +sin ^(-1) ""(bx)/(c ) =sin ^(-1)""x where a^(2...

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  20. 2 tan ^(-1) (Cos x) = tan ^(-1) (2 "cosec"x)

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