Solve cos(pi/2)+{left(cos(pi/4)right)}^2

$$\cos ( \frac{ \pi }{ 2 } ) + { \left( \cos ( \frac{ \pi }{ 4 } ) \right) }^{ 2 }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Get the value of \cos(\frac{\pi }{2}) from trigonometric values table.

$$0+\left(\cos(\frac{\pi }{4})\right)^{2}$$

Get the value of \cos(\frac{\pi }{4}) from trigonometric values table.

$$0+\left(\frac{\sqrt{2}}{2}\right)^{2}$$

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

$$0+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}$$

Anything plus zero gives itself.

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

The square of \sqrt{2} is 2.

$$\frac{2}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$