The smallest positive value of `x` (in radians) satisfying the equation `(log)_(cosx)((sqrt(3))/2sinx)=2-(log)_(secx)(tanx)` is (a)`pi/(12)` (b) `pi/6` (c) `pi/4` (d) `pi/3`

Explanation

To solve the equation \( \log_{\cos x} \left( \frac{\sqrt{3}}{2} \sin x \right) = 2 - \log_{\sec x} (\tan x) \), we will follow these steps:

### Step 1: Rewrite the logarithm on the right-hand side
We know that \( \log_{\sec x} (\tan x) \) can be rewritten using the change of base formula:
\[ \log_{\sec x} (\tan x) = \frac{\log(\tan x)}{\log(\sec x)} \]
Since \( \sec x = \frac{1}{\cos x} \), we can express \( \log(\sec x) \) as \( -\log(\cos x) \). Thus,
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