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Prove the following: 3sin^–1 x = sin^–1 ...

Prove the following: `3sin^–1 x = sin^–1 (3x – 4x^3), x in [–1/2 , 1/2]`

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PSEB-INVERSE TRIGONOMETRIC FUNCTIONS-Exercise
  1. If sin^-1x=y, then -pi/2< y < pi/2, is it true or false?

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  2. tan^-1 sqrt3 - sec^-1 (-2) is equal to :

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  3. Prove the following: 3sin^–1 x = sin^–1 (3x – 4x^3), x in [–1/2 , 1/2]

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  4. Prove the following: 3cos^–1 x = cos^–1 (4x^3 – 3x), x in [1/2,1]

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  5. Prove the following: tan^–1 (2/11) + tan^-1 (7/24) = tan^-1 (1/2)

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  6. Prove that : 2tan^-1 (1/2) + tan^-1 (1/7) = tan^-1 (31/17)

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  7. Write the following function in the simplest form: tan^-1 ((sqrt(1+cos...

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

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  9. Write the following function in the simplest form : tan^-1 (1/sqrt(x^2...

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  10. Write the following function in the simplest form: tan -1 ((cosx - sin...

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  11. Write the following function in the simplest form: tan^-1 (x/sqrt(a^2 ...

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

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  13. Find the value of the following: tan^-1[2 cos(2sin^-1(1/2))]

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

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

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

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

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  18. The value of sin^-1 (sin (2π/3)) is :

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  19. The value of tan^-1 (tan (3π/4)) is :

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  20. Find the value of tan(sin^-1 frac{3}{5} + cot^-1 frac{3}{2}).

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