Solve sqrt{3}sin60^circ+cos60^circsin30^circ

$$\sqrt { 3 } \sin 60 ^ { \circ } + \cos 60 ^ { \circ } \sin 30 ^ { \circ }$$

Evaluate

$$\frac{7}{4}=1.75$$

Short Solution Steps

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

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

Express \sqrt{3}\times \frac{\sqrt{3}}{2} as a single fraction.

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

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

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

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

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply \frac{\sqrt{3}\sqrt{3}}{2} times \frac{2}{2}.

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

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

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

Do the multiplications in 2\sqrt{3}\sqrt{3}+1.

$$\frac{6+1}{4}$$

Do the calculations in 6+1.

$$\frac{7}{4}$$