Question

Find the exact value using a half angle identity: cos 7 pi/8

Answer 1

`\cos (7\pi)/(8)=-(1)/(2)\sqrt[]{2+\sqrt[]{2}}`

Step-by-step explanation:

Given

`\cos (7\pi)/(8)`

Using the identity:

`\begin{gathered} \cos ((7\pi)/(2*4))=\pm\sqrt[]{(1+\cos(7\pi)/(4))/(2)} \\ \\ =-\sqrt[]{\frac{1+\frac{1}{\sqrt[]{2}}}{2}} \\ \\ =-\sqrt[]{\frac{2+\sqrt[]{2}}{4}} \\ \\ =-(1)/(2)\sqrt[]{2+\sqrt[]{2}} \end{gathered}`