Solve sin45^circ+3tan30^circ+tan60^circ-2cos60^circ

$$\sin 45 ^ { \circ } + 3 \tan 30 ^ { \circ } + \tan 60 ^ { \circ } - 2 \cos 60 ^ { \circ }$$

Evaluate

$$\frac{\sqrt{2}}{2}+2\sqrt{3}-1\approx 3.171208396$$

Short Solution Steps

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

$$\frac{\sqrt{2}}{2}+3\tan(30)+\tan(60)-2\cos(60)$$

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

$$\frac{\sqrt{2}}{2}+3\times \frac{\sqrt{3}}{3}+\tan(60)-2\cos(60)$$

Cancel out 3 and 3.

$$\frac{\sqrt{2}}{2}+\sqrt{3}+\tan(60)-2\cos(60)$$

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

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 2\sqrt{3} times \frac{2}{2}.

$$\frac{\sqrt{2}}{2}+\frac{2\times 2\sqrt{3}}{2}-2\cos(60)$$

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

$$\frac{\sqrt{2}+2\times 2\sqrt{3}}{2}-2\cos(60)$$

Do the multiplications in \sqrt{2}+2\times 2\sqrt{3}.

$$\frac{\sqrt{2}+4\sqrt{3}}{2}-2\cos(60)$$

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

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.

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

Since \frac{\sqrt{2}+4\sqrt{3}}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

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