Evaluate : `int_0^(pi/6)cosxcos2xdx`

Explanation

To evaluate the integral \( I = \int_0^{\frac{\pi}{6}} \cos x \cos 2x \, dx \), we can use the product-to-sum identities for cosine functions. The relevant identity is:

\[ \cos A \cos B = \frac{1}{2} \left( \cos(A + B) + \cos(A - B) \right) \]

### Step 1: Apply the Product-to-Sum Identity
Using the identity, we rewrite the integral:
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