Solve (-sqrt{2})^2+(1/2)^0-sqrt{2}cos45^circ

$$( - \sqrt { 2 } ) ^ { 2 } + ( \frac { 1 } { 2 } ) ^ { 0 } - \sqrt { 2 } \cos 45 ^ { \circ }$$

Evaluate

$$2$$

Solution Steps

Calculate -\sqrt{2} to the power of 2 and get \left(\sqrt{2}\right)^{2}.

$$\left(\sqrt{2}\right)^{2}+\left(\frac{1}{2}\right)^{0}-\sqrt{2}\cos(45)$$

Calculate \frac{1}{2} to the power of 0 and get 1.

$$\left(\sqrt{2}\right)^{2}+1-\sqrt{2}\cos(45)$$

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

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

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

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Divide 2 by 2 to get 1.

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

Subtract 1 from 1 to get 0.

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

The square of \sqrt{2} is 2.

$$2$$