Chapter 7.2, Problem 16E

To determine

To write: the expression as the sine, cosine or tangent of an angle and then find the exact value.

Answer to Problem 16E

  $\cos 10°\cos 80°-\sin 10°\sin 80°=\cos 90°=0$ .

Explanation of Solution

Given information:

Given expression,

  $\cos 10°\cos 80°-\sin 10°\sin 80°$ .

Calculation:

Based on the sum formula of cosine function, we have

  $\cos u\cos v-\sin u\sin v=\cos \left(u+v\right)$

Replace $u$ with $80°$ and $v$ with $10°$ and simplify.

  $\begin{array}{c}\cos 10°\cos 80°-\sin 10°\sin 80°=\cos \left(10°+80°\right)\\ =\cos 90°\\ =0\end{array}$ .