Chapter 14.3, Problem 17PPS

To determine

To calculate:The value of $\cos \left(-\frac{\pi }{12}\right)$

Answer to Problem 17PPS

  $\frac{\sqrt{3}+1}{2\sqrt{2}}.$

Explanation of Solution

Given information:

We know that, the given expression is $\cos \left(-\frac{\pi }{12}\right)$

Formula used:

  $\begin{array}{l}\cos (-\text{θ})=\cos \text{θ}\\ \text{cos(A+B)}=\text{cosAcosB}-\text{sinAsinB}.\end{array}$

Calculation:

  $\begin{array}{l}\text{cos}\frac{\text{π}}{\text{12}}=\text{cos}\left(\frac{\text{π}}{\text{4}}-\frac{\text{π}}{\text{6}}\right)\\ =\cos \frac{\text{π}}{\text{4}}\cos \frac{\text{π}}{\text{6}}+\sin \frac{\text{π}}{\text{4}}\sin \frac{\text{π}}{6}\\ =\frac{1}{\sqrt{2}}\times \frac{\sqrt{2}}{2}+\frac{1}{\sqrt{2}}\times \frac{1}{2}\\ =\frac{\sqrt{3}+1}{2\sqrt{2}}\end{array}$