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

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

A

2

B

4

C

`1//2`

D

`1//4`

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

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

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

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

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

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

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

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

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

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

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

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

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  13. The arithmetic mean of the non-zero solutions of the equation "Tan"^...

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  14. The number of real solutions of Tan^(-1)sqrt(x(x+1))+Sin^(-1)sqrt(x^(2...

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  15. An integral solution of the equation Tan^(-1)x+Tan^(-1)(1//y)=Tan^(-1)...

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  16. The solution of "Sin"^(-1)(2a)/(1+a^(2))-"Cos"^(-1)(1-b^(2))/(1+b^(2))...

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  17. If Sin^(-1)(tanpi//4)-Sin^(-1)sqrt(3//x)-pi//6=0, then x is a root of ...

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  18. If theta=Sin^(-1)x+Cos^(-1)x-Tan^(-1)x,0lexle1, then the smallest inte...

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  19. The trigonometric equation Sin^(-1)x=2Sin^(-1)a, has a solution for

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  20. If Cos^(-1)x=Tan^(-1)x, then sin(Cos^(-1)x)=

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