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sin^(-1)((2x)/(1+x^(2))) = 2 tan^(-1)x f...

`sin^(-1)((2x)/(1+x^(2))) = 2 tan^(-1)x` for

A

`|x| ge 1`

B

`x ge 0`

C

`|x| le 1`

D

all `x in R`

Text Solution

Verified by Experts

The correct Answer is:
C
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MCGROW HILL PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -SOLVED EXAMPLES (LEVEL 1 SINGLE CORRECT ANSWER TYPE QUESTIONS)
  1. If sin^(-1) (x//5) + "cosec"^(-1)(5//4) = pi//2 then a values of x is

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  2. tan^(-1)(1//4) + tan^(-1) (2//9) is equal to

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  3. sin^(-1)((2x)/(1+x^(2))) = 2 tan^(-1)x for

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  4. cot^(-1)[(cos alpha)^(1//2)]-tan^(-1)[(cos alpha)^(1//2)]=x then sin x...

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  5. The trignometric equation sin^(-1)x = 2sin^(-1)a has a solution for

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  6. If 0 le x le 1 and theta = sin^(-1)x + cos^(-1)x - tan^(-1)x then

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  7. If x gt 0, y gt 0 and x gt y, then (tan^(-1)(x//y) + tan^(-1)[(x+y)//(...

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  8. The principal value of sin^(-1)(-sqrt(3)//2) + cos^(-1)(7pi//6) is

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  9. The value of cos^(-1)(-1//2) - 2sin^(-1)(1//2) + 3 cos^(-1) (-1//sqrt(...

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  10. If tan^(-1)(sqrt(1+x^(2))-1)/x=4 then x=

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  11. sec^(2)(tan^(-1)2) + "cosec"^(2)(cot^(-1)3) is equal to

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  12. The equation 2cos^(-1)x = sin^(-1) (2x sqrt(1-x^(2))) is valid for all...

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  13. If tan^(-1) 1/(1+2) + tan^(-1) 1/(1+(2)(3)) + tan^(-1)1/(1+(3)(4)) + …...

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  14. A value of x satisfying tan^(-1)(x+3) - tan^(-1)(x-3) = sin^(-1)(3//5)...

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  15. If x = "cosec"(tan^(-1)(cos(cot^(-1)(sec(sin^(-1)a))))), a in [0,1], t...

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  16. If sin^(-1) (sin(33pi)/7) + cos^(-1)(cos (46pi)/7) + tan^(-1)(-tan (13...

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  17. If 0 lt x lt 1, the number of solutions of the equations tan^(-1)(x-1)...

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  18. tan^(-1) (tan 4) - tan^(-1)(tan(-6)) + cos^(-1)(cos 10) is equal to

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  19. If x lt -1//sqrt(3), then the value of 3 tan^(-1)x - tan^(-1)(3x - x^(...

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  20. sin^(-1)(4//5) + sin^(-1)(5//13) + sin^(-1)(16//65) is equal to

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