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

`tan[1/2(sin^(- 1)((2x)/(1+x^2))+cos^(- 1)((1-y^2)/(1+y^2))]`

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Simplity tan{1/2sin^(-1)((2x)/(1+x^(2)))+1/2cos^(-1)(1-y^(2))/(1+y^(2))} , if xgtygt1 .

Prove that tan{1/2sin^(-1)((2x)/(1+x^(2)))+1/2cos^(-1)((1-y^(2))/(1+y^(2)))}=(x+y)/(1-xy) , where |x| lt 1,y gt 0 and xy lt 1 .

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

If 1/2"sin"^(-1)(2x)/(1+x^2)+1/2"cos"^(-1)(1-y^2)/(1+y^2)+1/3"tan"^(-1)(3z-z^3)/(1-3z^2)=5pi then x+y+z=

If sin^(-1)((2x)/(1+x^(2)))+cos^(-1)((1-x^(2))/(1+x^(2)))=4 tan^(-1) x then

If y=sin^(-1)((1-x^(2))/(1+x^(2)))+cos^(-1)((1-x^(2))/(1+x^(2))) find (dy)/(dx)

sin{tan^(-1)[(1-x^(2))/(2x)]+cos^(-1)[(1-x^(2))/(1+x^(2))]}=

sin [ tan^(-1). (1 - x^(2))/(2x) + cos^(-1) . (1-x^(2))/(1 + x^(2))] is

Prove that : 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^2y^2))+tan^(-1)((y^2-z^2)/(1+y^2z^2))+tan^(-1)((z^2-x^2)/(1+z^2x^2))

MODERN PUBLICATION-INVERSE - TRIGONOMETRIC FUNCTIONS-NCERT - FILE (Question from NCERT Book) (Exercise 2.2)
  1. Prove that: 3cos^(-1)x=cos^(-1)(4x^3-3x), x in [1/2,1]

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  2. Prove that: tan^(-1)2/(11)+tan^(-1)7/(24)=tan^(-1)1/2

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  3. Prove the following 2 tan^(-1). 1/2 +tan^(-1) . 1/7 = tan^(-1). ...

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  4. If x lt 0, then prove that cos^(-1) x = pi + tan^(-1). (sqrt(1 - x^(2)...

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  5. Prove that tan^(-1).(1)/(sqrt(x^(2) -1)) = (pi)/(2) - sec^(-1) x, x gt...

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  6. convert in the simplest form: tan^(-1)(sqrt((1-cosx)/(1+cosx))), x lt ...

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

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  8. tan^(-1)""(x)/(sqrt(a^(2)-x^(2))),|x|lt a

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  9. Write the following function in the simplest form: tan^(-1)((3a^2x-x^3...

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  10. Find the values of each of the following : tan^(-1) [ 2 cos (2 s...

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  11. Evaluate cot(tan^(-1)a+cot^(-1)a)

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  12. tan[1/2(sin^(- 1)((2x)/(1+x^2))+cos^(- 1)((1-y^2)/(1+y^2))]

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  13. If sin (sin^(-1).(1)/(5) + cos^(-1) x) = 1, then find the value of x

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  14. If tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=pi/4, then find the val...

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  15. Sin^(-1)("sin"(2pi)/3)=

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  16. tan^(-2)tan((3pi)/(4))

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  17. Prove that : tan(sin^(-1) (3/5 + cot^(-1), 3/2) = 17/6

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  18. cos^(-1)(cos((7pi)/6)) is equal to

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  19. sin(pi/3-sin^(-1)(-1/2))is equal to(A) 1/2 (B) 1/3 (C) 1/4 (D) 1

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  20. tan^(-1)sqrt(3)-cot^(-1)(-sqrt(3))is equal to(A) pi (B) -pi/2 (C) 0 (D...

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