Question

1. simplify the expression ( 2sin 3\thetacos 3\theta ) by using a double - angle formula.

Explanation:

Step1: Recall double - angle formula

The double - angle formula for sine is \(\sin(2\alpha)=2\sin\alpha\cos\alpha\).

Step2: Substitute \(\alpha = 3\theta\)

Let \(\alpha=3\theta\). Then \(2\sin(3\theta)\cos(3\theta)=\sin(2\times3\theta)\).

Answer:

\(\sin(6\theta)\)