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

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

Evaluate

$$-\frac{\sqrt{3}}{3}\approx -0.577350269$$

Solution Steps

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

$$\sqrt{3}\times \frac{1}{2}-\tan(\frac{\pi }{6})+\sqrt{3}\cos(\frac{\pi }{3})-\sqrt{3}\tan(\frac{\pi }{4})$$

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

$$\sqrt{3}\times \frac{1}{2}-\frac{\sqrt{3}}{3}+\sqrt{3}\cos(\frac{\pi }{3})-\sqrt{3}\tan(\frac{\pi }{4})$$

Combine \sqrt{3}\times \frac{1}{2} and -\frac{\sqrt{3}}{3} to get \frac{1}{6}\sqrt{3}.

$$\frac{1}{6}\sqrt{3}+\sqrt{3}\cos(\frac{\pi }{3})-\sqrt{3}\tan(\frac{\pi }{4})$$

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

$$\frac{1}{6}\sqrt{3}+\sqrt{3}\times \frac{1}{2}-\sqrt{3}\tan(\frac{\pi }{4})$$

Combine \frac{1}{6}\sqrt{3} and \sqrt{3}\times \frac{1}{2} to get \frac{2}{3}\sqrt{3}.

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

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

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

Combine \frac{2}{3}\sqrt{3} and -\sqrt{3} to get -\frac{1}{3}\sqrt{3}.

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