Question

calculate the following without use of calculator 2cos^2 22.5​

Answer 1

Answer:

$\frac{\sqrt2}2 + 1$

Step-by-step explanation:

We can use the following identity to determine the value of this function.

$\cos(2\alpha) = 2\cos^2(\alpha) - 1$

In our case, $\alpha = 22.5$

$2\cos^2(22.5)\\\to 2\cos^2(22.5) - 1 + 1\\\to \cos(2 \times 22.5) + 1\\\to \cos(45) + 1\\\to \frac{\sqrt2}2 + 1$