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Find the range of tan^(-1)((2x)/(1+x^2))...

Find the range of `tan^(-1)((2x)/(1+x^2))`

A

`[-(pi)/(4), (pi)/(4)]`

B

`(-(pi)/(2), (pi)/(2))`

C

`(-(pi)/(2), (pi)/(4)]`

D

`[(pi)/(4), (pi)/(2)]`

Text Solution

Verified by Experts

The correct Answer is:
A
`1 + x^(2) ge 2 |x|`
or `(2|x|)/(1 + x^(2)) le 1`
or `-1 le (2x)/(1 + x^(2)) le 1`
`rArr tan^(-1) ((2x)/(1 + x^(2))) in [-(pi)/(4), (pi)/(4)]`
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CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-Exercise (Single)
  1. Range of f(x)=sin^(-1)x+tan^(-1)x+sec^(-1)x is

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  2. The value of lim(|x| rarr oo) cos (tan^(-1) (sin (tan^(-1) x))) is equ...

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  3. Find the range of tan^(-1)((2x)/(1+x^2))

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  4. Equation [cot^(-1) x] + 2 [tan^(-1) x] = 0, where [.] denotes the grea...

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  5. The number of integral values of k for which the equation sin^(-1)x+ta...

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  6. The range of the values of p for which the equation sin cos^(-1) ( co...

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  7. The number of the solutions of the equation 2 sin^(-1) sqrt(x^(2) + x ...

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  8. complete solution set of tan^(-1) (sin^(-1) x) gt 1 is

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  9. The trigonometric equation sin^(-1)x=2sin^(-1)a has a solution for all...

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  10. The number of solution of equation sin^(-1)x+nsin^(-1)(1-x)=(mpi)/2,w ...

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  11. If |cos^(-1) ((1 -x^(2))/(1 + x^(2)))| lt (pi)/(3), then

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  12. The value of sin^(-1) (sin 12) + cos^(-1) (cos 12) is equal to

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  13. The value of the expression sin^(-1)(sin(22pi)/7)cos^(-1)(cos(5pi)/3)+...

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  14. The value of sin^(-1)("cos"(cos^(-1)(cosx)+sin^(-1)(sinx))), where x i...

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  15. If alpha in (-(3pi)/2,-pi) , then the value of tan^(-1)(cotalpha)-cot^...

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  16. tan^-1[(cos x)/(1+sin x)] is equal to

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  17. If f(x)=x^(11)+x^9-x^7+x^3+1 and f(sin^(-1)(sin8)=alpha,alpha is const...

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  18. If sin^(-1) : [-1, 1] rarr [(pi)/(2), (3pi)/(2)] and cos^(-1) : [-1, 1...

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  19. Which of the following is the solution set of the equation 2cos^(-1)x=...

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  20. Which of the following is the solution set of the equat where x in (0,...

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