Final answer:
To solve the equation sin(2\(\theta\)) = cos(\(\theta\)), use the trigonometric identity sin(2\(\theta\)) = 2sin(\(\theta\))cos(\(\theta\)), then divide both sides by cos(\(\theta\)) and take the inverse sine of 1/2 to find \(\theta\).
Step-by-step explanation:
To solve the equation sin(2\(\theta\)) = cos(\(\theta\)), you can use the trigonometric identity which states that sin(2\(\theta\)) = 2sin(\(\theta\))cos(\(\theta\)). By using this identity, you can write the given equation as 2sin(\(\theta\))cos(\(\theta\)) = cos(\(\theta\)). If cos(\(\theta\)) is not zero, you can divide both sides of the equation by cos(\(\theta\)) to get 2sin(\(\theta\)) = 1.
Then, you would solve for \(\theta\) by taking the inverse sine (arcsin) of 1/2. If cos(\(\theta\)) is zero, which happens at \(\theta\) = \(\frac{\pi}{2}\) and \(\frac{3\pi}{2}\), you have an additional set of solutions to consider.