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Prove that tan ^(-1) x+tan ^(-1) ((2 x)/...

Prove that `tan ^(-1) x+tan ^(-1) ((2 x)/(1-x^2))=tan ^(-1)((3 x-x^3)/(1-3 x^2)),|x|lt1/sqrt3`

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V PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. Express tan^-1(frac(cosx)(1-sinx)) in the simplest Form.

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  2. Express cot ^(-1)(1/(sqrt(x^2-1))),|x|gt1 in the simplest form.

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  3. Prove that tan ^(-1) x+tan ^(-1) ((2 x)/(1-x^2))=tan ^(-1)((3 x-x^3)/(...

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  4. Find the value of cos(sec ^(-1) x+cosec^(-1) x),|x| ge 1

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  5. Prove that 3 sin ^(-1) x = sin^(-1) (3x - 4x^3), x in [-1/2,1/2]

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  6. prove that 3 cos^(-1) x = cos^(-1) (4x^3 - 3x), x in [1/2,1]

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

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

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

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  10. Write the following functions in the simplest form : tan^(-1)(1/sqrt...

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  11. Write the following functions in the simplest form : tan^(-1) sqrt((...

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  12. Write the following functions in the simplest form : tan^(-1)((cos x...

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  13. Write the following functions in the simplest form : tan^(-1) (x/sqr...

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

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  15. Find the values of each of the following tan ^(-1)[2 cos (2 sin ^(-1) ...

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

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  17. Find the values of the following tan frac(1)(2) [sin^(-1)((2x)/(1+x...

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

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  19. If tan^(-1) ((x-1)/(x-2)) + tan^(-1) ((x+1)/(x+2)) = pi/4. then find t...

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

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