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If Sin^(-1)((2a)/(1+a^(2)))+Sin^(-1)((2b...

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

A

`(a+b)/(1-ab)`

B

`(a-b)/(1+ab)`

C

`(ab-1)/(a+b)`

D

`(ab+1)/(a-b)`

Text Solution

Verified by Experts

The correct Answer is:
A
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DIPTI PUBLICATION ( AP EAMET)-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE 1
  1. tan(Cos^(-1)1//x)=sin(Cot^(-1)1//2),"if "xne0 then x =

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

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

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  4. If Tan^(-1)((x-1)/(x-2))+Cot^(-1)((x+2)/(x+1))=pi/4, then x =

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

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

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

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

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  9. If Cos^(-1)x=Cot^(-1)(4//3)+Tan^(-1)(1//7) then x =

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  10. If Sin^(-1)(3//5)+Sin^(-1)(5//13)=Sin^(-1)x, then x =

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  11. If "Cos"^(-1)3/5-"Sin"^(-1)4/5=Cos^(-1)x then x =

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  12. If Sin^(-1)(3/x)+Sin^(-1)(4/x)=pi/2 then x =

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  13. If Cot^(-1)x+Sin^(-1)(1//sqrt5)=pi//4, then the value of x is

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  14. If Cosec^(-1)x=2Cot^(-1)7+Cos^(-1)(3//5) then the value of x is

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  15. If Tan^(-1)(secx+tanx)=pi//4+kx then k =

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  16. Solve 3Sin^(-1)((2x)/(1+x^(2))) - 4 Cos^(-1)((1-x^(2))/(1+x^(2)))+2Tan...

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  17. If 1/2Sin^(-1)[(3Sin2theta)/(5+4cos2theta)]=Tan^(-1)x, then x =

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  18. If Sec^(-1)(x/a)-Sec^(-1)(x/b)=Sec^(-1)(b)-Sec^(-1)(a)andaneb, then x ...

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  19. If a=sin(Cot^(-1)x)andb=cot(Sin^(-1)x) where xgt0, then 1//x^(2)-x^(2)...

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  20. If Tan^(-1)2x+Tan^(-1)3x=pi//4, then x =

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