Solve 1-sin(45)cos(45)

$$1- \sin ( 45 ) \cos ( 45 )$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

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

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

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

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

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

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

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

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

The square of \sqrt{2} is 2.

$$1-\frac{2}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$1-\frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

Subtract \frac{1}{2} from 1 to get \frac{1}{2}.

$$\frac{1}{2}$$