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If tan A=1//2, tan B=1//3, then prove th...

If `tan A=1//2, tan B=1//3`, then prove that `cos 2A=sin2B`.

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To prove that \( \cos 2A = \sin 2B \) given \( \tan A = \frac{1}{2} \) and \( \tan B = \frac{1}{3} \), we will calculate both sides of the equation using trigonometric identities. ### Step-by-Step Solution: **Step 1: Calculate \( \cos 2A \)** We use the formula for \( \cos 2A \) in terms of \( \tan A \): \[ ...
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