Řešení - Trigonometry

The period of trigonometric functions is 360 degrees.

$$\cot \left(405°\right)=\cot \left(405-360°\right)$$

Subtracting one integer from another.

$$\cot \left(405-360°\right)=\cot \left(45°\right)$$

The cotangent of an angle is equal to the cosine of the angle divided by the sine of the angle.

$$\cot \left(45°\right)=\frac{\cos \left(45°\right)}{\sin \left(45°\right)}$$

Computing the cosine of 45 degrees.

$$\frac{\cos \left(45°\right)}{\sin \left(45°\right)}=\frac{\frac{\sqrt{2}}{2}}{\sin \left(45°\right)}$$

Computing the sine of 45 degrees.

$$\frac{\frac{\sqrt{2}}{2}}{\sin \left(45°\right)}=\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}$$

Dividing the same numbers.

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