Solve tan(30^circ)*tan(60^circ)-sqrt{2}cos(45^circ)

$$\tan ( 30 ^ { \circ } ) \cdot \tan ( 60 ^ { \circ } ) - \sqrt{ 2 } \cos ( 45 ^ { \circ } )$$

Evaluate

$$0$$

Short Solution Steps

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

$$\frac{\sqrt{3}}{3}\tan(60)-\sqrt{2}\cos(45)$$

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

$$\frac{\sqrt{3}}{3}\sqrt{3}-\sqrt{2}\cos(45)$$

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

$$\frac{\sqrt{3}\sqrt{3}}{3}-\sqrt{2}\cos(45)$$

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

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

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

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

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

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

Divide 2 by 2 to get 1.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3}{3}.

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

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

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

Do the multiplications in \sqrt{3}\sqrt{3}-3.

$$\frac{3-3}{3}$$

Do the calculations in 3-3.

$$\frac{0}{3}$$

Zero divided by any non-zero number gives zero.

$$0$$