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Find the value of: tan1/2[sin^(-1)(2x)/(...

Find the value of: `tan1/2[sin^(-1)(2x)/(1+x^2)+cos^(-1)(1-y^2)/(1+y^2)],|x|<1, y >0` and `x y" "<" "1`

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To solve the problem, we need to find the value of: \[ \tan\left(\frac{1}{2}\left[\sin^{-1}(2x)/(1+x^2) + \cos^{-1}(1-y^2)/(1+y^2)\right]\right) \] where \(|x| < 1\), \(y > 0\), and \(xy < 1\). ...
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NAGEEN PRAKASHAN ENGLISH-INVERES TRIGONOMETRIC FUNCTIONS-Exericse 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 that: 2tan^(-1)1/2+tan^(-1)1/7=tan^(-1)(31)/(17)

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  4. Write the following function in the simplest form: tan^(-1)(sqrt(1+x^2...

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  5. tan^(- 1)(1/(sqrt(x^2-1))),|x|gt1

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  6. Express each of the following in the simplest form: tan^(-1){sqrt((...

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  7. tan^(-1)((cosx-sinx)/(cosx+sinx))=pi/4-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. For the principal values, evaluate each of the following: tan^(-1){2co...

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  11. Find the value of: cot(tan^(-1)a+cot^(-1)a)

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  12. Find the value of: tan1/2[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 xdot

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  14. tan^-1 (x-1)/(x-2) + tan^-1 (x+1)/(x+2)=pi/4. find X

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  15. Find the value of sin^(-1)(sin((2pi)/3))

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  16. Find the value of tan^(-1)(tan((3pi)/4))

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  17. Find the value of tan(sin^(-1)3/5+cot^(-1)3/2)

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  18. cos^(-1)(cos(7pi)/6)is equal to(a) (7pi)/6 (B) (5pi)/6 (C) pi/3 (D) pi...

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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 ...

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