Solve cos30^circ/tan30^circsin60^circ

$$\frac { \cos 30 ^ { \circ } } { \tan 30 ^ { \circ } \sin 60 ^ { \circ } }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

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

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

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

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

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

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

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

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

Divide \frac{\sqrt{3}}{2} by \frac{\sqrt{3}\sqrt{3}}{3\times 2} by multiplying \frac{\sqrt{3}}{2} by the reciprocal of \frac{\sqrt{3}\sqrt{3}}{3\times 2}.

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

Cancel out 2\sqrt{3} in both numerator and denominator.

$$\frac{3}{\sqrt{3}}$$

Rationalize the denominator of \frac{3}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

$$\frac{3\sqrt{3}}{3}$$

Cancel out 3 and 3.

$$\sqrt{3}$$