simplify to an expression of the form (a sin(θ)). 8 sin(π/4) 8 cos(π/4) additional materials ebook double…

Explanation:

Step1: Recall double - angle formula

We know that $\sin(2\alpha)=2\sin\alpha\cos\alpha$.

Step2: Rewrite the given expression

The given expression is $8\sin(\frac{\pi}{4})8\cos(\frac{\pi}{4}) = 32\times2\sin(\frac{\pi}{4})\cos(\frac{\pi}{4})$.

Step3: Apply double - angle formula

Since $\alpha=\frac{\pi}{4}$, then $2\sin(\frac{\pi}{4})\cos(\frac{\pi}{4})=\sin(2\times\frac{\pi}{4})=\sin(\frac{\pi}{2})$. So the expression becomes $32\sin(\frac{\pi}{2})$.

Answer:

$32\sin(\frac{\pi}{2})$