Solve cos(-pi/6+pi/3)*tan(-pi/3+pi/2)

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

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Combine -\frac{\pi }{6} and \frac{\pi }{3} to get \frac{1}{6}\pi .

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

Get the value of \cos(\frac{1}{6}\pi ) from trigonometric values table.

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

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

$$\frac{\sqrt{3}}{2}\tan(\frac{1}{6}\pi )$$

Get the value of \tan(\frac{1}{6}\pi ) from trigonometric values table.

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

Multiply \frac{\sqrt{3}}{2} times \frac{\sqrt{3}}{3} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Multiply 2 and 3 to get 6.

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

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$