Solve 1/2-cos^2pi/8=

$$\frac { 1 } { 2 } - \cos ^ { 2 } \frac { \pi } { 8 } =$$

Evaluate

$$-\frac{\sqrt{2}}{4}\approx -0.353553391$$

Short Solution Steps

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

$$\frac{1}{2}-\left(\frac{\sqrt{\sqrt{2}+2}}{2}\right)^{2}$$

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

$$\frac{1}{2}-\frac{\left(\sqrt{\sqrt{2}+2}\right)^{2}}{2^{2}}$$

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

$$\frac{1}{2}-\frac{\sqrt{2}+2}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{1}{2}-\frac{\sqrt{2}+2}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply \frac{1}{2} times \frac{2}{2}.

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

Since \frac{2}{4} and \frac{\sqrt{2}+2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-\left(\sqrt{2}+2\right)}{4}$$

Do the multiplications in 2-\left(\sqrt{2}+2\right).

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

Do the calculations in 2-\sqrt{2}-2.

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