Trigonometry Examples

$2 (\cos (x) (\cos (3 x)) - (\sin (x) \sin (3 x))) = - 1$

Step 1

Simplify $2 (\cos (x) (\cos (3 x)) - (\sin (x) \sin (3 x)))$ .

Tap for more steps...

Step 1.1

Remove parentheses.

$2 (\cos (x) \cos (3 x) - \sin (x) \sin (3 x)) = - 1$

Step 1.2

Simplify by multiplying through.

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$2 (\cos (x) \cos (3 x)) + 2 (- \sin (x) \sin (3 x)) = - 1$

Step 1.2.2

Multiply $- 1$ by $2$ .

$2 \cos (x) \cos (3 x) - 2 \sin (x) \sin (3 x) = - 1$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = \frac{π}{6} + \frac{π n}{2}, \frac{π}{3} + \frac{π n}{2}$ , for any integer $n$

Step 3