Solve cos(45^circ)(sin(30^circ)-cos(30^circ))=

$$\cos ( 45 ^ { \circ } ) ( \sin ( 30 ^ { \circ } ) - \cos ( 30 ^ { \circ } ) )=$$

Evaluate

$$\frac{\sqrt{2}-\sqrt{6}}{4}\approx -0.258819045$$

Solution Steps

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

$$\frac{\sqrt{2}}{2}\left(\sin(30)-\cos(30)\right)$$

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

$$\frac{\sqrt{2}}{2}\left(\frac{1}{2}-\cos(30)\right)$$

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

$$\frac{\sqrt{2}}{2}\left(\frac{1}{2}-\frac{\sqrt{3}}{2}\right)$$

Since \frac{1}{2} and \frac{\sqrt{3}}{2} have the same denominator, add them by adding their numerators.

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

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

$$\frac{\sqrt{2}\left(1+\sqrt{3}\right)}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{2}\left(1+\sqrt{3}\right)}{4}$$

Use the distributive property to multiply \sqrt{2} by 1+\sqrt{3}.

$$\frac{\sqrt{2}+\sqrt{2}\sqrt{3}}{4}$$

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

$$\frac{\sqrt{2}+\sqrt{6}}{4}$$