Chapter 14.3, Problem 1BCYP

To determine

To calculate:The value of $\cos (-15°)$

Answer to Problem 1BCYP

  $\frac{\sqrt{3}+1}{2\sqrt{2}}.$

Explanation of Solution

Given information:

We know that, the given expression is $\cos (-15°)$ .

Formula used:

  $\cos (-\text{θ})=\cos \text{θ},\cos (\text{A}-\text{B})=\cos \text{A}\cos \text{B}+\sin \text{A}\sin \text{B}$

Calculation:

  $\begin{array}{l}\text{cos(}-{15}^{\circ })=\text{cos(}{15}^{\circ })\\ =\text{cos(}{45}^{\circ }-{30}^{\circ })\\ =\text{cos}{45}^{\circ }\text{cos}{30}^{\circ }+\text{sin}{45}^{\circ }\sin {30}^{\circ }.\\ =\frac{\sqrt{3}+1}{2\sqrt{2}}.\end{array}$