Solve tan(30)*tan(60)*cos(60)

$$\tan ( 30 ) \times \tan ( 60 ) \times \cos ( 60 )$$

Evaluate

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

Solution Steps

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

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

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

$$\frac{\sqrt{3}}{3}\sqrt{3}\cos(60)$$

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

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

Express \frac{\sqrt{3}}{3}\sqrt{3} as a single fraction.

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

Multiply \frac{\sqrt{3}\sqrt{3}}{3} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Multiply 3 and 2 to get 6.

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

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

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