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Prove that 3 tan^(-1) x= {(tan^(-1) ((...

Prove that
`3 tan^(-1) x= {(tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " -(1)/(sqrt3) lt x lt (1)/(sqrt3)),(pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x gt (1)/(sqrt3)),(-pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x lt - (1)/(sqrt3)):}`

A

`3 tan^(-1)x`

B

`-pi+3tan^(-1)x`

C

`pi+3tan^(-1)x`

D

none of these

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS -Exercise
  1. Prove that 3 tan^(-1) x= {(tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if ...

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  2. Prove that 3 tan^(-1) x= {(tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if ...

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  3. Prove that 3 tan^(-1) x= {(tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if ...

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  4. If 0 le x lt oo, then cos^(-1)((1-x^(2))/(1+x^(2))) equals

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  5. If -oo lt x le 0 then cos ^(-1)((1-x^(2))/(1+x^(2)))equals

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  6. If x in [-1,1] then sin^(-1)((2x)/(1+x^(2))) equals

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  7. If x in (1,oo) then sin^(-1)((2x)/(1+x^(2))) equals

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  8. If x in (-oo,-1) then sin^(-1)((2x)/(1+x^(2))) equals

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  9. If sin^(-1)((2x)/(1+x^(2)))+cos^(-1)((1-x^(2))/(1+x^(2)))=4 tan^(-1) x...

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  10. If 1 tan^(-1) x + sin^(-1).(2x)/(1 + x^(2)) is independent of x, then

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  11. If tan^(-1) x + tan^(-1)y + tan^(-1)z= pi then x + y + z is equal to

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  12. The value of cos(tan^-1 (tan 2)) is

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  13. If sec^(-1) x = cosec^(-1) y, then find the value of cos^(-1).(1)/(x) ...

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  14. Let cos(2 tan^(-1) x)=1/2 then the value of x is

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  15. If tan^(-1) . x/pi lt pi/3 , x in N , then the maximum value of x is

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  16. Range of the function f(x)= cos^(-1)(-{x}) , where {.} is fractional...

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  17. sec^(-1)(sin x) exist if

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  18. cot((pi)/(4)-2 cot^(-1)3) is :

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  19. Solve [cot^(-1) x] + [cos^(-1) x] =0, where [.] denotes the greatest i...

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  20. Find the sum cot^(-1) 2 + cot^(-1) 8 + cot^(-1) 18 + ...oo

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