Solve sin(30)cos(45)-cos(60)sin(60)

$$\sin ( 30 ) \cos ( 45 ) - \cos ( 60 ) \sin ( 60 )$$

Evaluate

$$\frac{\sqrt{2}-\sqrt{3}}{4}\approx -0.079459311$$

Short Solution Steps

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

$$\frac{1}{2}\cos(45)-\cos(60)\sin(60)$$

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

$$\frac{1}{2}\times \frac{\sqrt{2}}{2}-\cos(60)\sin(60)$$

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

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

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

$$\frac{\sqrt{2}}{2\times 2}-\frac{1}{2}\sin(60)$$

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

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

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

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

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{2}}{2\times 2}-\frac{\sqrt{3}}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Expand 2\times 2.

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

Since \frac{\sqrt{2}}{4} and \frac{\sqrt{3}}{4} have the same denominator, subtract them by subtracting their numerators.

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