Question

How do I find the value of $\cos 45°$?

Answer 1

Find the value of $\cos 45°$.

It's known that,

$$\begin{gathered} \cos 2x=2{\cos }^{2}x-1 \\ \Rightarrow {\cos }^{2}x=\frac{1}{2}(1+\cos 2x) \\ \Rightarrow \cos x=\frac{\sqrt{2}}{2}\sqrt{1+\cos 2x} \end{gathered}$$

Substitute the angle value:

$\begin{array}{rcl}\cos (2x45°)& =& \cos 90°\\ & =& 0\end{array}$

So, the value can be calculated as:

$\cos 45°=\frac{\sqrt{2}}{2}$

Hence, the value of $\cos 45°$ is $\frac{\sqrt{2}}{2}$.