`if A=( theta :2 cos^(2)theta + sin theta le 2)` and
`b= {theta :(pi)/(2)le theta le (3pi)/(2)}`, then `A cap B ` is equal to

Options

A. `{theta:pi//2le thetale 5 pi //6}`
B. `{theta:pilethetale 3pi//2}`
C. `{theta:pi//2le theta le 5pi/6} cup {theta: pi le theta 3pi //2}`
D. none of these

Explanation

To solve the problem, we need to find the intersection of the sets A and B defined as follows:

1. **Set A**: \( A = \{ \theta : 2 \cos^2 \theta + \sin \theta \leq 2 \} \)
2. **Set B**: \( B = \{ \theta : \frac{\pi}{2} \leq \theta \leq \frac{3\pi}{2} \} \)

### Step 1: Simplify the inequality for Set A

We start with the inequality from Set A:
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