Solve tan30+cot30/sin30

$$\frac { \tan 30 + \cot 30 } { \sin 30 }$$

Evaluate

$$\frac{8\sqrt{3}}{3}\approx 4.618802154$$

Solution Steps

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

$$\frac{\frac{\sqrt{3}}{3}+\cot(30)}{\sin(30)}$$

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

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

Combine \frac{\sqrt{3}}{3} and \sqrt{3} to get \frac{4}{3}\sqrt{3}.

$$\frac{\frac{4}{3}\sqrt{3}}{\sin(30)}$$

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

$$\frac{\frac{4}{3}\sqrt{3}}{\frac{1}{2}}$$

Divide \frac{4}{3}\sqrt{3} by \frac{1}{2} by multiplying \frac{4}{3}\sqrt{3} by the reciprocal of \frac{1}{2}.

$$\frac{4}{3}\sqrt{3}\times 2$$

Multiply \frac{4}{3} and 2 to get \frac{8}{3}.

$$\frac{8}{3}\sqrt{3}$$