Solve cos60^circ/sin60^circ+cot60^circ*tan60^circ

$$\frac { \cos 60 ^ { \circ } } { \sin 60 ^ { \circ } + \cot 60 ^ { \circ } } \cdot \tan 60 ^ { \circ }$$

Evaluate

$$\frac{3}{5}=0.6$$

Solution Steps

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

$$\frac{\frac{1}{2}}{\sin(60)+\cot(60)}\tan(60)$$

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

$$\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}+\cot(60)}\tan(60)$$

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

$$\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{3}}\tan(60)$$

Combine \frac{\sqrt{3}}{2} and \frac{\sqrt{3}}{3} to get \frac{5}{6}\sqrt{3}.

$$\frac{\frac{1}{2}}{\frac{5}{6}\sqrt{3}}\tan(60)$$

Express \frac{\frac{1}{2}}{\frac{5}{6}\sqrt{3}} as a single fraction.

$$\frac{1}{2\times \frac{5}{6}\sqrt{3}}\tan(60)$$

Rationalize the denominator of \frac{1}{2\times \frac{5}{6}\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{3}}{2\times \frac{5}{6}\left(\sqrt{3}\right)^{2}}\tan(60)$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{3}}{2\times \frac{5}{6}\times 3}\tan(60)$$

Multiply 2 and \frac{5}{6} to get \frac{5}{3}.

$$\frac{\sqrt{3}}{\frac{5}{3}\times 3}\tan(60)$$

Multiply \frac{5}{3} and 3 to get 5.

$$\frac{\sqrt{3}}{5}\tan(60)$$

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

$$\frac{\sqrt{3}}{5}\sqrt{3}$$

Express \frac{\sqrt{3}}{5}\sqrt{3} as a single fraction.

$$\frac{\sqrt{3}\sqrt{3}}{5}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{3}{5}$$