Řešení - Trigonometry

The period of trigonometric functions is 360 degrees.

$$\tan \left(585°\right)=\tan \left(585-360°\right)$$

Subtracting one integer from another.

$$\tan \left(585-360°\right)=\tan \left(225°\right)$$

Reflecting the number with respect to 360 degrees.

$$\tan \left(225°\right)=\tan \left(360-135°\right)$$

The period of trigonometric functions is 360 degrees.

$$\tan \left(360-135°\right)=\tan \left(360-135-360°\right)$$

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

$$\tan \left(360-135-360°\right)=\tan \left(-135°\right)$$

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

$$\tan \left(-135°\right)=\frac{\sin \left(-135°\right)}{\cos \left(-135°\right)}$$

Computing the sine of a negative angle.

$$\frac{\sin \left(-135°\right)}{\cos \left(-135°\right)}=\frac{-\sin \left(135°\right)}{\cos \left(-135°\right)}$$

Computing the cosine of a negative angle.

$$\frac{-\sin \left(135°\right)}{\cos \left(-135°\right)}=\frac{-\sin \left(135°\right)}{\cos \left(135°\right)}$$

Placing the minus sign in front of a fraction.

$$\frac{-\sin \left(135°\right)}{\cos \left(135°\right)}=-\frac{\sin \left(135°\right)}{\cos \left(135°\right)}$$

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

$$-\frac{\sin \left(135°\right)}{\cos \left(135°\right)}=-\tan \left(135°\right)$$

Reflecting the number with respect to 360 degrees.

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

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

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

Reflecting the sine function with respect to 180 degrees.

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

Reflecting the cosine function with respect to 180 degrees.

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

Placing the minus sign in front of a fraction.

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

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

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

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

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

Computing the sine of 45 degrees.

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

Computing the cosine of 45 degrees.

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

Dividing the same numbers.

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