Solve sqrt{2}sin45^circ+1/2cos60^circ

$$\sqrt { 2 } \sin 45 ^ { \circ } + \frac { 1 } { 2 } \cos 60 ^ { \circ }$$

Evaluate

$$\frac{5}{4}=1.25$$

Short Solution Steps

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

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

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

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

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

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

Multiply \frac{1}{2} and \frac{1}{2} to get \frac{1}{4}.

$$\frac{\sqrt{2}\sqrt{2}}{2}+\frac{1}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply \frac{\sqrt{2}\sqrt{2}}{2} times \frac{2}{2}.

$$\frac{2\sqrt{2}\sqrt{2}}{4}+\frac{1}{4}$$

Since \frac{2\sqrt{2}\sqrt{2}}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{2\sqrt{2}\sqrt{2}+1}{4}$$

Do the multiplications in 2\sqrt{2}\sqrt{2}+1.

$$\frac{4+1}{4}$$

Do the calculations in 4+1.

$$\frac{5}{4}$$