Solve sin45^circ-sin30^circ+cos60^circ

$$\sin 45 ^ { \circ } - \sin 30 ^ { \circ } + \cos 60 ^ { \circ }$$

Evaluate

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Short Solution Steps

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

$$\frac{\sqrt{2}}{2}-\sin(30)+\cos(60)$$

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

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

Since \frac{\sqrt{2}}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

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

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

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

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

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

Do the calculations in \sqrt{2}-1+1.

$$\frac{\sqrt{2}}{2}$$