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Write the following functions in the sim...

Write the following functions in the simplest form :
`tan^(-1)(1/sqrt(x^2 -1)), |x| gt 1`

Text Solution

Verified by Experts

Put x = sec`theta, theta sec^(-1)x`
Then `tan^(-1)(1/sqrt(x^2-1)) = tan^(-1)(1/sqrt(sec^2 theta -1)) = tan^(-1)(1/tan theta)`
`= tan^(-1) cot theta = tan^(-1)tan(pi/2- theta) = pi/2-sec^(-1)x`
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A N EXCEL PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. prove that 3 cos^(-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 2 tan^(-1)(1/2) + tan^(-1)(1/7) = tan^(-1)(31/17)

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

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

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

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

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

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

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  10. Find the value of tan^(-1)[2 cos(2sin^(-1)frac(1)(2) )]

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

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

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  13. If sin(sin^-1(frac(1)(5))+cos^-1(x))=1

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

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

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  16. Find the values of the following : tan^(-1)(tan frac (3pi)4)

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  17. Evaluate tan(sin^-1frac(3)(5)+cot^-1frac(3)(2))

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  18. find the value of cos^-1cos((7pi)/3)

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  19. Find sin(pi/3-sin^(-1)(-1/2)) =

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  20. Find tan^(-1) sqrt3 -sec^(-1)(-2)

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