Solve cos^2pi/8

$$\cos ^ { 2 } \pi / 8$$

Evaluate

$$\frac{\sqrt{2}}{4}+\frac{1}{2}\approx 0.853553391$$

Solution Steps

Get the value of \cos(\frac{\pi }{8}) from trigonometric values table.

$$\left(\frac{\sqrt{\sqrt{2}+2}}{2}\right)^{2}$$

To raise \frac{\sqrt{\sqrt{2}+2}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(\sqrt{\sqrt{2}+2}\right)^{2}}{2^{2}}$$

Calculate \sqrt{\sqrt{2}+2} to the power of 2 and get \sqrt{2}+2.

$$\frac{\sqrt{2}+2}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\sqrt{2}+2}{4}$$