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If Tan^(-1)(1//(a-1))=Tan^(-1)(1//x)+Tan...

If `Tan^(-1)(1//(a-1))=Tan^(-1)(1//x)+Tan^(-1)[1//(a^(2)-x+1)]`, then x =

A

`2aora^(2)+a+1`

B

`aora^(2)-a+1`

C

`aora^(2)+2a+1`

D

none of these

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Verified by Experts

The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE 1
  1. If 2Tan^(-1)x+Sec^(-1)x=pi//2 then x =

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  2. If "Tan"^(-1)a/x+"Tan"^(-1)b/x=pi/2 then x =

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  3. If Tan^(-1)(1//(a-1))=Tan^(-1)(1//x)+Tan^(-1)[1//(a^(2)-x+1)], then x ...

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  4. If "Sin"^(-1)5/x+"Sin"^(-1)12/x=pi/2, then x =

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  5. If Sin^(-1)(x//5)+Cosec^(-1)(5//4)=pi//2 then a value of x is

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  6. If Sin^(-1)x-Cos^(-1)x = (pi)/6 then find x.

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  7. If Sin^(-1)x+Sin^(-1)(1-x)=Cos^(-1)x then x =

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  8. The equation Sin^(-1)x-Cos^(-1)x=Cos^(-1)(sqrt3//2) has

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  9. If Tan^(-1)(x+1)+Tan^(-1)(x-1)=Tan^(-1)(4//7), then x =

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  10. A solution of the equation Tan^(-1)(1+x)+Tan^(-1)(1-x)=pi//2 is

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  11. Sin^(-1)x-Cos^(-1)x=Sin^(-1)(3x-2),"if "xgt0 then x =

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  12. If 2Tan^(-1)(cosx)=Tan^(-1)(2cosecx) then x =

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  13. tan(Cos^(-1)1//x)=sin(Cot^(-1)1//2),"if "xne0 then x =

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  14. The value of x where xgt0andtan(Sec^(-1)(1/x))=sin(Tan^(-1)2) is

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  17. If Tan^(-1)((x+1)/(x-1))+Tan^(-1)((x-1)/x)=pi+Tan^(-1)(-7), then x =

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  18. If 3Tan^(-1)(1/(2+sqrt3))-Tan^(-1)(1/x)=Tan^(-1)(1/3), then x =

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  19. If "Cot"^(-1)4/3+"Cot"^(-1)5/3=Tan^(-1)k, then k =

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  20. If "Sec"^(-1)1/(sqrt(1-x^(2)))+"Cot"^(-1)(sqrt(1-x^(2)))/x=Sin^(-1)k, ...

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