CPM Homework Help : PCT Problem 9-105

Solve $8\cos\left(x\right)\sin\left(x\right)=2$ for all values of $x$ .

Hint:

Use the double-angle identity:
$2\cos\left(x\right)·\sin\left(x\right)=\sin\left(2x\right)$

Step 1:

$4\left(2\cos\left(x\right)·\sin\left(x\right)\right)=2$

Step 2:

$4\sin\left(2x\right)=2$

Step 3:

$\sin(2x)=\frac{1}{2}$

Step 4:

$2x=\frac{\pi }{6}+2\pi n,\therefore x=\frac{\pi }{12}+\pi n$

$2x=\frac{5\pi }{6}+2\pi n,\therefore x=\frac{5\pi }{12}+\pi n$