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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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PRADEEP PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. If sin^-1 x = y, then 0 le y le pi

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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+x^2...

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

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  9. Write the following functions in the simplest form: tan^-1((sqrt(1-c...

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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 functions in the simplest form: tan^-1(x/(sqrt(a...

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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 each 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. Find the values of each of the expressions sin^-1(sin((2pi)/3))

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

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  20. Find the values of each of the expressions tan(sin^-1(3/5) + cot^-1(...

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