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

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

A

`2tan^(-1)x`

B

`-2tan^(-1)x`

C

`pi-2 tan^(-1)x`

D

`pi+2 tan^(-1)x`

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The correct Answer is:
A
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OBJECTIVE RD SHARMA-INVERSE TRIGONOMETRIC FUNCTIONS -Exercise
  1. If x gt (1)/sqrt(3) then tan^(-1) (3x-x^(3))/(1-3x^(2)) equals

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  2. If x lt -(1)/sqrt(3) , then tan^(-1)(3x-x^(3))/(1-3x^(2)) equals

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

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

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

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

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

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

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

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

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

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  12. If sec^(-1)x=cosec^(-1) y then cos^(-1)(1/x)+cos^(-1)(1/y)=

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

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

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

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

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  17. The value of cot(pi/4-2 cot^(-1)3) is

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  18. [cot^(-1)x][cos^(-1) x] =0 where x is non negative and [.] is he great...

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  19. The sum of the series cot^-1 2 + cot^-1 8 +cot^-1 18+cot^-1 32...........

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  20. If cos^(-1)(x)/(2)+cos^(-1)(y)/(3)=theta then the maximum of 9x^(2)-12...

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