Řešení - Trigonometry

Reflecting the number with respect to 360 degrees.

$$\cot \left(285°\right)=\cot \left(360-75°\right)$$

The period of trigonometric functions is 360 degrees.

$$\cot \left(360-75°\right)=\cot \left(360-75-360°\right)$$

Removing or simplifying the same numbers on the top and bottom of a fraction.

$$\cot \left(360-75-360°\right)=\cot \left(-75°\right)$$

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

$$\cot \left(-75°\right)=\frac{\cos \left(-75°\right)}{\sin \left(-75°\right)}$$

Computing the cosine of a negative angle.

$$\frac{\cos \left(-75°\right)}{\sin \left(-75°\right)}=\frac{\cos \left(75°\right)}{\sin \left(-75°\right)}$$

Computing the sine of a negative angle.

$$\frac{\cos \left(75°\right)}{\sin \left(-75°\right)}=\frac{\cos \left(75°\right)}{-\sin \left(75°\right)}$$

Placing the minus sign in front of a fraction.

$$\frac{\cos \left(75°\right)}{-\sin \left(75°\right)}=-\frac{\cos \left(75°\right)}{\sin \left(75°\right)}$$

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

$$-\frac{\cos \left(75°\right)}{\sin \left(75°\right)}=-\cot \left(75°\right)$$