Solve -2sin30^circ+sqrt{3}cos30^circ

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

Evaluate

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

Short Solution Steps

Get the value of \sin(30) 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.

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