Solve 2sin45^circ-tan45^circ/4tan60^circ

$$\frac { 2 \sin 45 ^ { \circ } - \tan 45 ^ { \circ } } { 4 \tan 60 ^ { \circ } }$$

Evaluate

$$\frac{\sqrt{3}\left(\sqrt{2}-1\right)}{12}\approx 0.059786578$$

Solution Steps

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

$$\frac{2\times \frac{\sqrt{2}}{2}-\tan(45)}{4\tan(60)}$$

Cancel out 2 and 2.

$$\frac{\sqrt{2}-\tan(45)}{4\tan(60)}$$

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

$$\frac{\sqrt{2}-1}{4\tan(60)}$$

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

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

Rationalize the denominator of \frac{\sqrt{2}-1}{4\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\left(\sqrt{2}-1\right)\sqrt{3}}{4\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\left(\sqrt{2}-1\right)\sqrt{3}}{4\times 3}$$

Multiply 4 and 3 to get 12.

$$\frac{\left(\sqrt{2}-1\right)\sqrt{3}}{12}$$

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

$$\frac{\sqrt{2}\sqrt{3}-\sqrt{3}}{12}$$

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

$$\frac{\sqrt{6}-\sqrt{3}}{12}$$