Solve 2sin45^circcos45^circ/7

$$\frac { 2 \sin 45 ^ { \circ } \cos 45 ^ { \circ } } { 7 }$$

Evaluate

$$\frac{1}{7}\approx 0.142857143$$

Solution Steps

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

$$\frac{2\times \frac{\sqrt{2}}{2}\cos(45)}{7}$$

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

$$\frac{2\times \frac{\sqrt{2}}{2}\times \frac{\sqrt{2}}{2}}{7}$$

Multiply \frac{\sqrt{2}}{2} and \frac{\sqrt{2}}{2} to get \left(\frac{\sqrt{2}}{2}\right)^{2}.

$$\frac{2\times \left(\frac{\sqrt{2}}{2}\right)^{2}}{7}$$

To raise \frac{\sqrt{2}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{2\times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}}}{7}$$

Express 2\times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}} as a single fraction.

$$\frac{\frac{2\left(\sqrt{2}\right)^{2}}{2^{2}}}{7}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\frac{\left(\sqrt{2}\right)^{2}}{2}}{7}$$

Express \frac{\frac{\left(\sqrt{2}\right)^{2}}{2}}{7} as a single fraction.

$$\frac{\left(\sqrt{2}\right)^{2}}{2\times 7}$$

The square of \sqrt{2} is 2.

$$\frac{2}{2\times 7}$$

Multiply 2 and 7 to get 14.

$$\frac{2}{14}$$

Reduce the fraction \frac{2}{14} to lowest terms by extracting and canceling out 2.

$$\frac{1}{7}$$