If `tanA=1/7a n d tanB=1/3` , show that `cos2A=sin4Bdot`

Explanation

To solve the problem, we need to show that \( \cos 2A = \sin 4B \) given that \( \tan A = \frac{1}{7} \) and \( \tan B = \frac{1}{3} \).

### Step 1: Find \( \sin A \) and \( \cos A \)

Given \( \tan A = \frac{1}{7} \), we can represent this in a right triangle where the opposite side is 1 and the adjacent side is 7.

Using the Pythagorean theorem:
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