Question

10\sin(\theta)\cos(\theta)=5\sin(2\theta) for angle \theta in standard position. true false

Explanation:

Step1: Use double - angle formula

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

Step2: Substitute the formula

Substitute \(\sin(2\theta)=2\sin\theta\cos\theta\) into the right - hand side of the given equation. Then \(5\sin(2\theta)=5\times(2\sin\theta\cos\theta)\).

Step3: Simplify the expression

\(5\times(2\sin\theta\cos\theta)=10\sin\theta\cos\theta\), which is equal to the left - hand side of the given equation \(10\sin\theta\cos\theta\).

Answer:

True