Solve sin(60^circ)*cos(30^circ)-sin(30^circ)*cos(60^circ)=

$$\sin ( 60 ^ { \circ } ) \times \cos ( 30 ^ { \circ } ) - \sin ( 30 ^ { \circ } ) \times \cos ( 60 ^ { \circ } ) =$$

Evaluate

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

Solution Steps

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

$$\frac{\sqrt{3}}{2}\cos(30)-\sin(30)\cos(60)$$

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

$$\frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2}-\sin(30)\cos(60)$$

Multiply \frac{\sqrt{3}}{2} and \frac{\sqrt{3}}{2} to get \left(\frac{\sqrt{3}}{2}\right)^{2}.

$$\left(\frac{\sqrt{3}}{2}\right)^{2}-\sin(30)\cos(60)$$

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

$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}-\sin(30)\cos(60)$$

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

$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}-\frac{1}{2}\cos(60)$$

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

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

Multiply \frac{1}{2} and \frac{1}{2} to 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, subtract them by subtracting 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.

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

Subtract \frac{1}{4} from \frac{3}{4} to get \frac{1}{2}.

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