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if cos^-1 x > sin^-1 x, then x belon...

if `cos^-1 x > sin^-1 x`, then `x` belongs to the interval

A

`(-oo,0)-1,0)`

B

`(-1,0)`

C

`[(0,(1)/sqrt(2))`

D

`[-1,(1)/sqrt(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
We know that `cos^(-1)x and sin^(-1)x` exist for `x in[-1,1]`
Now
`cos^(-1)xgtsin^(-1)x`

`rarr cos^(-1)x gt (pi)/(2)-cos^(-1)x`
`rarr 2 cos^(-1)xgt(pi)/(2)rarr cos^(-1)xgt(pi)/(4)xgt(pi)/(4)rarrx in [-1,(1)/sqrt(2))`
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OBJECTIVE RD SHARMA-INVERSE TRIGONOMETRIC FUNCTIONS -Section I - Solved Mcqs
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  2. If sin^(-1)sqrt(x^2+2x + 1) + sec^(-1)sqrt(x^2 + 2x + 1) = pi/2; x!= 0...

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  3. if cos^-1 x > sin^-1 x, then x belongs to the interval

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  7. Which of the following is the solution set of the equation sin^-1 x = ...

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  9. The value of a for which a x^2+sin^(-1)(x^2-2x+2)+cos^(-1)(x^2-2x+2)=1...

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  10. The value of x that satisfies tan^(-1)(tan -3)=tan^(2)x is

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  11. If cos^(-1)((n)/(2pi)) gt(2pi)/(3) then maximum and minimum values of ...

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  12. The set of values of k for which x^2 - kx + sin^-1 (sin 4) > 0 for all...

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  13. The set of values of x satisfying |sin^(- 1)x|lt|cos^(- 1)x|,is

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  14. If [cot^(-1)x]+[cos^(-1)x]=0 , where [" "] denotes the greatest intege...

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  15. The number of real solutions of tan^(-1)sqrt(x(x+1))+sin^(-1)sqrt(x^2+...

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  16. The number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin^...

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  17. The number of solution of sin{sin^(-1)(log(1//2)x)}+2|cos{sin^(-1)(x...

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  18. The value of "tan"(sin^(-1)("cos"(sin^(-1)x)))"tan"(cos^(-1)(sin(cos^(...

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  19. Value of x satisfying tan(sec^(- 1)x)=sin(cos^(- 1)(1/(sqrt(5))))

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  20. Exhaustive set of values of parameter 'a' so that sin^(-1)x-tan^(-1)x=...

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