Answer:
[tex]\text{ cos }\frac{\pi}{4}\text{ = }\frac{\sqrt[]{2}}{2}[/tex]
Explanation:
Here, we want to find the value of cos pi/4
We have this as follows:
[tex]\begin{gathered} \text{ sin(2}\times\frac{\pi}{4})\text{ = 2sin(}\frac{\pi}{4})\cos \frac{\pi}{4} \\ \\ =\text{ sin}\frac{\pi}{2}\text{ = 2sin}\frac{\pi}{4}\cos \frac{\pi}{4} \end{gathered}[/tex]
Now, we have to divide both sides by 2sin(pi/4)
We have this as:
[tex]\begin{gathered} \text{ cos}\frac{\pi}{4}\text{ = }\frac{\sin \frac{\pi}{2}}{2\sin \frac{\pi}{4}}=\text{ }\frac{1}{2\times\frac{1}{\sqrt[]{2}}} \\ \\ \cos \text{ }\frac{\pi}{4}\text{ = }\frac{1}{\frac{2}{\sqrt[]{2}}}\text{ = 1}\times\frac{\sqrt[]{2}}{2}\text{ = }\frac{\sqrt[]{2}}{2} \end{gathered}[/tex]
