Solve cos(pi/6)-sqrt{2}sin(pi/4)+sqrt{3}tan(pi/3)

$$\cos ( \frac{ \pi }{ 6 } ) - \sqrt{ 2 } \sin ( \frac{ \pi }{ 4 } ) + \sqrt{ 3 } \tan ( \frac{ \pi }{ 3 } )$$

Evaluate

$$\frac{\sqrt{3}}{2}+2\approx 2.866025404$$

Short Solution Steps

Get the value of \cos(\frac{\pi }{6}) from trigonometric values table.

$$\frac{\sqrt{3}}{2}-\sqrt{2}\sin(\frac{\pi }{4})+\sqrt{3}\tan(\frac{\pi }{3})$$

Get the value of \sin(\frac{\pi }{4}) from trigonometric values table.

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

Express \sqrt{2}\times \frac{\sqrt{2}}{2} as a single fraction.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

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

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

Get the value of \tan(\frac{\pi }{3}) from trigonometric values table.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

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

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

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

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

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

$$\frac{\sqrt{3}-2+6}{2}$$

Do the calculations in \sqrt{3}-2+6.

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