Solve sin^260^circ-cos^230^circ

$$\sin ^ { 2 } 60 ^ { \circ } - \cos ^ { 2 } 30 ^ { \circ }$$

Evaluate

$$0$$

Solution Steps

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

$$\left(\frac{\sqrt{3}}{2}\right)^{2}-\left(\cos(30)\right)^{2}$$

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

$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}-\left(\cos(30)\right)^{2}$$

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

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

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

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

The square of \sqrt{3} is 3.

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

Calculate 2 to the power of 2 and get 4.

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

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

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

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

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

The square of \sqrt{3} is 3.

$$\frac{3}{2^{2}}-\frac{3}{4}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{3}{4}-\frac{3}{4}$$

Subtract \frac{3}{4} from \frac{3}{4} to get 0.

$$0$$