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