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

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