Solve (tan(30)+sin(30))cos(30)

$$( \tan ( 30 ) + \sin ( 30 ) ) \cos ( 30 )$$

Evaluate

$$\frac{\sqrt{3}+2}{4}\approx 0.933012702$$

Short Solution Steps

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

$$\left(\frac{\sqrt{3}}{3}+\sin(30)\right)\cos(30)$$

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{\sqrt{3}}{3} times \frac{2}{2}. Multiply \frac{1}{2} times \frac{3}{3}.

$$\left(\frac{2\sqrt{3}}{6}+\frac{3}{6}\right)\cos(30)$$

Since \frac{2\sqrt{3}}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{2\sqrt{3}+3}{6}\cos(30)$$

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

$$\frac{2\sqrt{3}+3}{6}\times \frac{\sqrt{3}}{2}$$

Multiply \frac{2\sqrt{3}+3}{6} times \frac{\sqrt{3}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2\sqrt{3}+3\right)\sqrt{3}}{6\times 2}$$

Multiply 6 and 2 to get 12.

$$\frac{\left(2\sqrt{3}+3\right)\sqrt{3}}{12}$$

Use the distributive property to multiply 2\sqrt{3}+3 by \sqrt{3}.

$$\frac{2\left(\sqrt{3}\right)^{2}+3\sqrt{3}}{12}$$

The square of \sqrt{3} is 3.

$$\frac{2\times 3+3\sqrt{3}}{12}$$

Multiply 2 and 3 to get 6.

$$\frac{6+3\sqrt{3}}{12}$$