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If cos^(-1)(cos 4)gt3x^(2)-4x then...

If `cos^(-1)(cos 4)gt3x^(2)-4x` then

A

`x in (-oo,(2-sqrt(6pi-8))/(3)`

B

`x in ((2+sqrt(6pi-87))/(3),oo)`

C

`x in ((2+sqrt(6pi-8))/(3),oo)`

D

`x in ((2-sqrt(p6pi-8))/(3),(2+sqrt(6pi-8))/(3)`

Text Solution

Verified by Experts

The correct Answer is:
`oo`
We have
`cos^(-1)(cos4)gt3x^(2)-4x`
`rarr cos^(-1)(cos(2pi-4))gt3x6(2)-4x`
`rarr 2pi -4 gt3x^(2)-4x^(2)`
`rarr 3x^(2)-4x-(2pi-4)lt0`
`rarr (2-sqrt(6pi-8))/(3)ltxlt(2+sqrt(6pi-8))/(3)`
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OBJECTIVE RD SHARMA-INVERSE TRIGONOMETRIC FUNCTIONS -Section I - Solved Mcqs
  1. The number of triple satisfying sin^(-1)x+cos^(-1)y+sin^(-1)z=2pi is

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  2. If sin^-1(sin 5)gtx^(2)-4x then

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  3. If cos^(-1)(cos 4)gt3x^(2)-4x then

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  4. The number of real solution (x,y) where |y|=sinx,y=cos^(-1)(cosx),-2pi...

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  5. If u=cot^(-1)sqrt(cos theta) -tan^(-1)sqrt(cos theta) then sin u=

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  6. tan(sec^(-1)x )=sin(cos^(-1)(1/sqrt5))

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  7. Number of integral solutions of the equation 2 sin^-1sqrt(x^2-x +1 )+ ...

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  8. If alpha, beta and gamma are the three angles with alpha = 2tan^(-1)(s...

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  9. If f(x) =cos^(-1)x+cos^(-1){(x/2+1/2sqrt(3-3x^(2)))} then f(2/3) equ...

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  10. The trigonometric equation sin^(-1)x=2sin^(-1)a has a solution for all...

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  11. If alpha is the only real root of the equation x^3 + bx^2 + cx + 1 = ...

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  12. If tan^(-1)(a/x)+tan^(-1)(b/x)+tan^(-1)(c /x)+tan^(-1)(d/x)=(pi)/(2) t...

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  13. If u=cot^(-1)sqrt(cos theta) -tan^(-1)sqrt(cos theta) then sin u=

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  14. If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi then the value of xsqrt(1-x^(2))+y...

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  15. if cos^(- 1)sqrt(p)+cos^(- 1)sqrt(1-p)+cos^(- 1)sqrt(1-q)=(3pi)/4 ,the...

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  16. The solution set of the equation sin^(-1)x=2 tan^(-1)x is

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  17. If cot(cos^(-1)x)=sec{tan^(-1)((a)/sqrt(b^(2)-a^(2)))} then x equals

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  18. tan^(-1)(C(1)x-y)/(c(1)+c(3)c(2))+..+tan^(-1)(1)/(c(n)) is equal top

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  19. If 0ltxlt1 then sqrt(1+x^(2))[{x cos (cot^(-1)x)+sin(cot^(-1)x}^(2)-1...

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  20. Sigma(r=1)^(infty) tan^(-1)(1)/(2r^(2))=t then tan t is equal to

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