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If 0 lt x lt 2 pi and |cos x| le sin x, ...

If `0 lt x lt 2 pi` and `|cos x| le sin x`, then

A

the set of all values of x is `[pi/4, (3pi)/4]`

B

the number of solutions that are integral multiple of `pi/2` is four

C

the sum of the largest and the smallest solution is `pi`

D

the set of all values of x is `x in [pi/4, pi/2) uu (pi/2, (3pi)/4]`

Text Solution

Verified by Experts

The correct Answer is:
A, C
It is easier to solve the inequality using graphical method. The graphs of `y=|cos x|` and `y= sin x` are as shown in the following figure.

From the figure, `|cos x| le sin x` for x in [pi/4, (3pi)/4]`
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CENGAGE-TRIGONOMETRIC EQUATIONS-Exercise (Multiple)
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  2. If 0 le x le 2pi, then 2^(cosec^(2) x) sqrt(1/2 y^(2) -y+1) le sqrt(2...

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  3. If the equation sin^2 x-a sin x + b = 0 has only one solution in (0, p...

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  4. If (cos e c^2theta-4)x^2+(cottheta+sqrt(3))x+cos^2(3pi)/2=0 holds true...

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  6. The value of x in (0,pi/2) satisfying the equation, (sqrt3-1)/sin x+ (...

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  7. If cos3theta=cos3alpha, then the value of sintheta can be given by +-s...

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  8. Which of the following sets can be the subset of the general solution ...

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  9. The values of x1 between 0 and 2pi , satisfying the equation cos3x+cos...

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  10. Which of the following set of values of x satisfies the equation 2^((2...

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  11. If 0 lt x lt 2 pi and |cos x| le sin x, then

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  12. The expression cos 3 theta + sin 3 theta + (2 sin 2 theta-3) (sin thet...

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  13. The solutions of the equation 1+(sin x - cos x)"sin" pi/4=2 "cos"^(2) ...

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  14. If xa n dy are positive acute angles such that (x+y) and (x-y) satisfy...

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  15. The solutions of the system of equations sin x sin y=sqrt(3)/4, cos x ...

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  16. Let f(x)=cos(a1+x)+1/2cos(a2+x)+1/(2^2)cos(a1+x)++1/(2^(n-1))cos(an+x)...

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  17. The equation 2sin^3theta+(2lambda-3)sin^2theta-(3lambda+2)sintheta-2la...

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  18. The system of equations tan x=a cot x, tan 2x=b cos y

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  19. (cos^2 x+1/(cos^2 x))(1+tan^2 2 y)(3+sin 3 z)=4, then y can take value...

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  20. Number of real solution of the equation (atn x+1) (tan x+3) (tan x+5) ...

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