Solve sin30+cos30/xsqrt{2}

$$\frac { \sin 30 + \cos 30 } { x \sqrt { 2 } }$$

Evaluate

$$\frac{\sqrt{2}\left(\sqrt{3}+1\right)}{4x}$$

Short Solution Steps

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

$$\frac{\frac{1}{2}+\cos(30)}{x\sqrt{2}}$$

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

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

Since \frac{1}{2} and \frac{\sqrt{3}}{2} have the same denominator, add them by adding their numerators.

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

Express \frac{\frac{1+\sqrt{3}}{2}}{x\sqrt{2}} as a single fraction.

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

Rationalize the denominator of \frac{1+\sqrt{3}}{2x\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\left(1+\sqrt{3}\right)\sqrt{2}}{2x\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\left(1+\sqrt{3}\right)\sqrt{2}}{2x\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{\left(1+\sqrt{3}\right)\sqrt{2}}{4x}$$

Use the distributive property to multiply 1+\sqrt{3} by \sqrt{2}.

$$\frac{\sqrt{2}+\sqrt{3}\sqrt{2}}{4x}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{2}+\sqrt{6}}{4x}$$