Solve sin(30^circ)cos(60^circ)+sin(60^circ)cos(30^circ)

$$\sin ( 30 ^ { \circ } ) \cos ( 60 ^ { \circ } ) + \sin ( 60 ^ { \circ } ) \cos ( 30 ^ { \circ } )$$

Evaluate

$$1$$

Solution Steps

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

$$\frac{1}{2}\cos(60)+\sin(60)\cos(30)$$

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

$$\frac{1}{2}\times \frac{1}{2}+\sin(60)\cos(30)$$

Multiply \frac{1}{2} and \frac{1}{2} to get \frac{1}{4}.

$$\frac{1}{4}+\sin(60)\cos(30)$$

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

$$\frac{1}{4}+\frac{\sqrt{3}}{2}\cos(30)$$

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

$$\frac{1}{4}+\frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2}$$

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

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

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.

$$1$$