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

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

A

29/27

B

`-29//27`

C

`27//11`

D

`-27//29`

Text Solution

Verified by Experts

The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE 1
  1. If Tan^(-1)((x+1)/(x-1))+Tan^(-1)((x-1)/x)=pi+Tan^(-1)(-7), then x =

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. If Tan^(-1)(x+1)+Tan^(-1)(x-1)=Tan^(-1)(8//31), then x =

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  18. If Tan^(-1)(1+x)+Tan^(-1)(1-x)=pi//4 then x =

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

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  20. (Tan^(-1)x)^(2)+(Cot^(-1)x)^(2)=5pi^(2)//8rArrx=

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