Final answer:
The expression 4 sin(θ) 4 cos(θ) simplifies to 8 sin(θ/2) by using the sine double angle formula sin(2θ) = 2 sin(θ) cos(θ), reflecting the fact that the original expression is twice the sine of half the angle.
Step-by-step explanation:
The student's question involves simplifying a mathematical expression using trigonometric identities. From the information provided, the task is to simplify the expression 4 sin(θ) 4 cos(θ) to the form (a sin(θ)). This simplification can be achieved using trigonometric formulas, specifically the double angle formulas. The formula for sine of a double angle is sin(2θ) = 2 sin(θ) cos(θ). Therefore, we can rewrite the given expression as 2 sin(2θ), where θ is θ/2 in this context. So our starting expression 4 sin(θ) 4 cos(θ) simplifies to 8 sin(θ/2).