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The range of the function , f (x) = ta...

The range of the function ,
`f (x) = tan^(-1) ((1+x)/(1 - x)) - tan^(-1) x ` is

A

`{pi//4}`

B

`{-(pi//4),3pi//4}`

C

`{pi//4, - (3pi//4)}`

D

`{3 pi//4}`

Text Solution

Verified by Experts

The correct Answer is:
C
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ARIHANT MATHS-INVERSE TRIGONOMETRIC FUNCTIONS-Exercise (Single Option Correct Type Questions)
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  3. Prove that: tan^(-1)(1/2tan2A)+tan^(-1)(cotA)+tan^(-1)(cot^3A)=0

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  4. Prove that : tan^-1(1/2) + tan^-1(1/5) + tan^-1(1/8) = pi/4

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  6. There exists a positive real number of x satisfying "cos"(tan^(-1)x)=x...

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  8. Number of solutions of the equation log(10) ( sqrt(5 cos^(-1) x -1 ...

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  9. Solve sin^(-1) x+ cos^(-1) x = sin^(-1) (3x -2)

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  12. The value of the angle tan^(-1) ( tan 65^(@) - 2 tan 40^(@)) in degree...

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  13. Prove that cotx - 2cot2x = tanx

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  14. The value of Sigma(r=1)^(infty) tan^(-1) ( 1/(r^(2) + 5r + 7)) is equ...

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  15. The range of the function , f (x) = tan^(-1) ((1+x)/(1 - x)) - tan^(...

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  16. Let g: Rvec(0,pi/3) be defined by g(x)=cos^(-1)((x^2-k)/(1+x^2)) . The...

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  17. Number of values of x satisfying simultaneously sin^(-1) x = 2 tan^(-1...

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  18. Number of values of x satisfying the equation cos ( 3 arc cos ( x-1)) ...

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  19. Which one of the following function contains only one integer in its ...

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