Solve 2tan^245^circ+cos45^circ+sin45^circ

$$2 \tan ^ { 2 } 45 ^ { \circ } + \cos 45 ^ { \circ } + \sin 45 ^ { \circ }$$

Evaluate

$$\sqrt{2}+2\approx 3.414213562$$

Solution Steps

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

$$2\times 1^{2}+\cos(45)+\sin(45)$$

Calculate 1 to the power of 2 and get 1.

$$2\times 1+\cos(45)+\sin(45)$$

Multiply 2 and 1 to get 2.

$$2+\cos(45)+\sin(45)$$

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

$$2+\frac{\sqrt{2}}{2}+\sin(45)$$

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

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

Combine \frac{\sqrt{2}}{2} and \frac{\sqrt{2}}{2} to get \sqrt{2}.

$$2+\sqrt{2}$$