Solve {l}{sqrt{2}sin45^circ}{-sqrt{3}cos30^circ}

$$\left. \begin{array} { l } { \sqrt { 2 } \sin 45 ^ { \circ } } \\ { - \sqrt { 3 } \cos 30 ^ { \circ } } \end{array} \right.$$

Evaluate

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

Short Solution Steps

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

$$\sqrt{2}\times \frac{\sqrt{2}}{2}-\sqrt{3}\cos(30)$$

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

$$\frac{\sqrt{2}\sqrt{2}}{2}-\sqrt{3}\cos(30)$$

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

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

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

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

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

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

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

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

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

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

Do the calculations in 2-3.

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

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

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