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If theta=Sin^(-1)x+Cos^(-1)x-Tan^(-1)x,0...

If `theta=Sin^(-1)x+Cos^(-1)x-Tan^(-1)x,0lexle1`, then the smallest interval in which `theta` lies is given by

A

`pi//4lethetalepi//2`

B

`-pi//4lethetale0`

C

`0lethetalepi//4`

D

`pi//2lethetale3pi//4`

Text Solution

Verified by Experts

The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE 1
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  2. If Tan^(-1)(1+x)+Tan^(-1)(1-x)=pi//4 then x =

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

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

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

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

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

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

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

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

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

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

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  13. The domain of Sin^(-1)x is

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  14. The domain of Cos^(-1)sqrt(2x) is

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  15. The domain of Sin^(-1)[log(2)(x^(2)//2)] is

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  16. The domain of Cos^(-1)(2/(2+sinx))"in "[0,2pi] is

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  17. The range of Sin^(-1)5x is

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  18. The range of Sin^(-1)x+Cos^(-1)x is

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  19. The range of Sin^(-1)x-Cos^(-1)x is

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  20. Two angles of a triangle are Cot^(-1)2andCot^(-1)3. Then the third ang...

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