If `f(x){(1-sin^2x)/(3cos^2x),xltpi/2 and a,x=pi/2 and (b(1-sinx))/(pi-2x)^2 , xgtpi/2`then `f(x)` is continuous at `x=pi/2,if` (a)`a=1/3,b=2` (b) `a=1/3,=8/3` (c)`a=2/3,b=8/3` (d) none of these

Explanation

To determine the values of \( a \) and \( b \) such that the function \( f(x) \) is continuous at \( x = \frac{\pi}{2} \), we will analyze the left-hand limit (LHL) and right-hand limit (RHL) of the function as \( x \) approaches \( \frac{\pi}{2} \).

### Step 1: Define the function pieces
The function \( f(x) \) is defined as follows:
- For \( x < \frac{\pi}{2} \):
\[ f(x) = \frac{1 - \sin^2 x}{3 \cos^2 x} \]
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