Question

Find the exact value of the expression:

$\cos 285°·\cos 195°$

Short answer

The exact value is $0$.

Step-by-step solution

Step 1. Given information.

Consider the given question,

$\cos 285°·\cos 195°$

We know $\cos a·\cos b=\frac{1}{2}\left[\cos \left(a-b\right)+\cos \left(a+b\right)\right]$.

Using the formula, we get,

$\cos 285°·\cos 195°=\frac{1}{2}\left[\cos \left(285-195\right)+\cos \left(285+195\right)\right]$

Step 2. Simplify the equation.

Continuing the above equation,

$$\begin{gathered} \cos 285°·\cos 195°=\frac{1}{2}\left[\cos \left(120°\right)+\cos \left(480°\right)\right] \\ \cos 285°·\cos 195°=\frac{1}{2}\left[-\frac{1}{2}+\left(-\frac{1}{2}\right)\right] \\ \cos 285°·\cos 195°=0 \end{gathered}$$