**Example Problem: Find sin(2A) and cos(2A)**Suppose \( A \) is an acute angle, and \[ \sin A = \frac{21}{29} \]\[ \cos A = \frac{20}{29} \]Find \( \sin 2A \) and \( \cos 2A \).\[ \sin 2A = \]\[ \cos 2A = \]### Solution:To find \( \sin 2A \) and \( \cos 2A \), we can use the following double-angle identities:1. \( \sin 2A = 2 \sin A \cos A \)2. \( \cos 2A = \cos^2 A - \sin^2 A \)Using the given values:\[ \sin A = \frac{21}{29} \]\[ \cos A = \frac{20}{29} \]First, calculate \( \sin 2A \):\[ \sin 2A = 2 \sin A \cos A \]\[ \sin 2A = 2 \left(\frac{21}{29}\right) \left(\frac{20}{29}\right) \]\[ \sin 2A = 2 \cdot \frac{420}{841} \]\[ \sin 2A = \frac{840}{841} \]Now, calculate \( \cos 2A \):\[ \cos 2A = \cos^2 A - \sin^2 A \]\[ \cos 2A = \left(\frac{20}{29}\right)^2 - \left(\frac{21}{29}\right)^2 \]\[ \cos 2A = \frac{400}{841} - \frac{441}{841} \]\[ \cos 2A = \frac{400 - 441}{841} \]\[ \cos 2A = \frac{-41}{841} \]Putting these results in the answer fields:\[ \sin 2A = \frac{840}{841} \]\[ \cos 2A = \frac{-41}{841} \]

Name: **Example Problem: Find sin(2A) and cos(2A)**Suppose \( A \) is an ac
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
Description: **Example Problem: Find sin(2A) and cos(2A)**Suppose \( A \) is an acute angle, and \[ \sin A = \frac{21}{29} \]\[ \cos A = \frac{20}{29} \]Find \( \sin 2A \) and \( \cos 2A \).\[ \sin 2A = \]\[ \cos 2A = \]### Solution:To find \( \sin 2A \) and \(