Solve cos45^circ/cos30^circ

$$\frac { \cos 45 ^ { \circ } } { \cos 30 ^ { \circ } }$$

Evaluate

$$\frac{\sqrt{6}}{3}\approx 0.816496581$$

Solution Steps

Get the value of \cos(45) from trigonometric values table.

$$\frac{\frac{\sqrt{2}}{2}}{\cos(30)}$$

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

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

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

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

Cancel out 2 in both numerator and denominator.

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

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

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

The square of \sqrt{3} is 3.

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

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

$$\frac{\sqrt{6}}{3}$$