Solve tan^260^circ-cos^230^circ

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

Evaluate

$$\frac{9}{4}=2.25$$

Solution Steps

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

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

The square of \sqrt{3} is 3.

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

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

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

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

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

The square of \sqrt{3} is 3.

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

Calculate 2 to the power of 2 and get 4.

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

Subtract \frac{3}{4} from 3 to get \frac{9}{4}.

$$\frac{9}{4}$$