Řešení - Trigonometry

Reflecting the number with respect to 360 degrees.

$$\cot \left(135°\right)=\cot \left(180-45°\right)$$

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

$$\cot \left(180-45°\right)=\frac{\cos \left(180-45°\right)}{\sin \left(180-45°\right)}$$

Reflecting the cosine function with respect to 180 degrees.

$$\frac{\cos \left(180-45°\right)}{\sin \left(180-45°\right)}=\frac{-\cos \left(45°\right)}{\sin \left(180-45°\right)}$$

Reflecting the sine function with respect to 180 degrees.

$$\frac{-\cos \left(45°\right)}{\sin \left(180-45°\right)}=\frac{-\cos \left(45°\right)}{\sin \left(45°\right)}$$

Placing the minus sign in front of a fraction.

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

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

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

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.

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