Solve cos30^circ+sin60^circ/1+cos60^circ+sin30^circ

$$\frac { \cos 30 ^ { \circ } + \sin 60 ^ { \circ } } { 1 + \cos 60 ^ { \circ } + \sin 30 ^ { \circ } }$$

Evaluate

$$\frac{\sqrt{3}}{2}\approx 0.866025404$$

Solution Steps

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

$$\frac{\frac{\sqrt{3}}{2}+\sin(60)}{1+\cos(60)+\sin(30)}$$

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

$$\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\cos(60)+\sin(30)}$$

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

$$\frac{\sqrt{3}}{1+\cos(60)+\sin(30)}$$

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

$$\frac{\sqrt{3}}{1+\frac{1}{2}+\sin(30)}$$

Add 1 and \frac{1}{2} to get \frac{3}{2}.

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

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

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

Add \frac{3}{2} and \frac{1}{2} to get 2.

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