Solve left(sin(60)right)^2+left(cos(60)right)^2=

$${ \left( \sin ( 60 ) \right) }^{ 2 } + { \left( \cos ( 60 ) \right) }^{ 2 } =$$

Evaluate

$$1$$

Solution Steps

Get the value of \sin(60) from trigonometric values table.

$$\left(\frac{\sqrt{3}}{2}\right)^{2}+\left(\cos(60)\right)^{2}$$

To raise \frac{\sqrt{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}+\left(\cos(60)\right)^{2}$$

Get the value of \cos(60) from trigonometric values table.

$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}+\left(\frac{1}{2}\right)^{2}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}+\frac{1}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Expand 2^{2}.

$$\frac{\left(\sqrt{3}\right)^{2}}{4}+\frac{1}{4}$$

Since \frac{\left(\sqrt{3}\right)^{2}}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{\left(\sqrt{3}\right)^{2}+1}{4}$$

The square of \sqrt{3} is 3.

$$\frac{3}{2^{2}}+\frac{1}{4}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{3}{4}+\frac{1}{4}$$

Add \frac{3}{4} and \frac{1}{4} to get 1.

$$1$$