Solve sin^230^circ+cos^230^circ=

$$\sin ^ { 2 } 30 ^ { \circ } + \cos ^ { 2 } 30 ^ { \circ } =$$

Evaluate

$$1$$

Solution Steps

Get the value of \sin(30) from trigonometric values table.

$$\left(\frac{1}{2}\right)^{2}+\left(\cos(30)\right)^{2}$$

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

$$\frac{1}{4}+\left(\cos(30)\right)^{2}$$

Get the value of \cos(30) from trigonometric values table.

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

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

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

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

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

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

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

The square of \sqrt{3} is 3.

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

Calculate 2 to the power of 2 and get 4.

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

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

$$1$$