Solve sqrt{3}cos(45)-sqrt{2}sin(60)

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

Evaluate

$$0$$

Short Solution Steps

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

$$\sqrt{3}\times \frac{\sqrt{2}}{2}-\sqrt{2}\sin(60)$$

Express \sqrt{3}\times \frac{\sqrt{2}}{2} as a single fraction.

$$\frac{\sqrt{3}\sqrt{2}}{2}-\sqrt{2}\sin(60)$$

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

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

Express \sqrt{2}\times \frac{\sqrt{3}}{2} as a single fraction.

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

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

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

Since \frac{\sqrt{3}\sqrt{2}}{2} and \frac{\sqrt{6}}{2} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Do the calculations in \sqrt{6}-\sqrt{6}.

$$\frac{0}{2}$$

Zero divided by any non-zero number gives zero.

$$0$$