Solve 2cos60^circ+sqrt{3}cos30^circ

$$2 \cos 60 ^ { \circ } + \sqrt { 3 } \cos 30 ^ { \circ }$$

Evaluate

$$\frac{5}{2}=2.5$$

Short Solution Steps

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

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

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

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

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

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.

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

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

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

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

$$\frac{2+3}{2}$$

Do the calculations in 2+3.

$$\frac{5}{2}$$