Chapter 7.3, Problem 8MCQ

To determine

To find: the exact value of given function by using sum or difference identity.

Answer to Problem 8MCQ

  $\frac{\sqrt{6}-\sqrt{2}}{4}$

Explanation of Solution

Given information:

  $\cos 75°$

Calculation:

Solve $\cos 75°$ as follows:

  $\begin{array}{c}\cos 75°=\cos \left(45°+30°\right)\left[\text{Rewrite 75}°\right]\end{array}$

  $\begin{array}{c}=\cos 45°\cos 30°-\sin 45°\sin 30°\left[\text{Use sum identity of cosine}\right]\end{array}$

  $\begin{array}{c}=\frac{\sqrt{2}}{2}\cdot \frac{\sqrt{3}}{2}-\frac{\sqrt{2}}{2}\cdot \frac{1}{2}\end{array}$

  $\begin{array}{c}=\frac{\sqrt{6}}{4}-\frac{\sqrt{2}}{4}\end{array}$

  $\begin{array}{c}=\frac{\sqrt{6}-\sqrt{2}}{4}\end{array}$

Thus the value of $\cos 75°$ is $\frac{\sqrt{6}-\sqrt{2}}{4}$ .