Solve 4sin30^circ+6cos60^circ/sqrt{3*cot60^circ}

$$\frac { 4 \sin 30 ^ { \circ } + 6 \cos 60 ^ { \circ } } { \sqrt { 3 } \cdot \cot 60 ^ { \circ } }$$

Evaluate

$$5$$

Solution Steps

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

$$\frac{4\times \frac{1}{2}+6\cos(60)}{\sqrt{3}\cot(60)}$$

Multiply 4 and \frac{1}{2} to get 2.

$$\frac{2+6\cos(60)}{\sqrt{3}\cot(60)}$$

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

$$\frac{2+6\times \frac{1}{2}}{\sqrt{3}\cot(60)}$$

Multiply 6 and \frac{1}{2} to get 3.

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

Add 2 and 3 to get 5.

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

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

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

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

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

Divide 5 by \frac{\sqrt{3}\sqrt{3}}{3} by multiplying 5 by the reciprocal of \frac{\sqrt{3}\sqrt{3}}{3}.

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

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

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

The square of \sqrt{3} is 3.

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

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

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

Multiply 3 and 5 to get 15.

$$\frac{15}{3}$$

Divide 15 by 3 to get 5.

$$5$$