Řešení - Trigonometry

The period of trigonometric functions is 360 degrees.

$$\tan \left(780°\right)=\tan \left(780-360°\right)$$

Subtracting one integer from another.

$$\tan \left(780-360°\right)=\tan \left(420°\right)$$

The period of trigonometric functions is 360 degrees.

$$\tan \left(420°\right)=\tan \left(420-360°\right)$$

Subtracting one integer from another.

$$\tan \left(420-360°\right)=\tan \left(60°\right)$$

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

$$\tan \left(60°\right)=\frac{\sin \left(60°\right)}{\cos \left(60°\right)}$$

Computing the sine of 60 degrees.

$$\frac{\sin \left(60°\right)}{\cos \left(60°\right)}=\frac{\frac{\sqrt{3}}{2}}{\cos \left(60°\right)}$$

Computing the cosine of 60 degrees.

$$\frac{\frac{\sqrt{3}}{2}}{\cos \left(60°\right)}=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}$$

Converting a fraction expression to multiplication by using the reciprocal of the denominator.

$$\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\sqrt{3}}{2}\times \frac{2}{1}$$

Multiplying two fractions together.

$$\frac{\sqrt{3}}{2}\times \frac{2}{1}=\frac{\sqrt{3}\times 2}{2\times 1}$$

Multiplication can be done in any order, and the result remains the same.

$$\frac{\sqrt{3}\times 2}{2\times 1}=\frac{\sqrt{3}\times 2}{1\times 2}$$

Distributing a fraction over multiplication.

$$\frac{\sqrt{3}\times 2}{1\times 2}=\frac{\sqrt{3}}{1}\times \frac{2}{2}$$

Distributing a fraction over multiplication.

$$\frac{\sqrt{3}\times 2}{1\times 2}=\frac{\sqrt{3}}{1}\times \frac{2}{2}$$

Dividing the same numbers.

$$\frac{\sqrt{3}}{1}\times \frac{2}{2}=\frac{\sqrt{3}}{1}\times 1$$

Distributing a fraction over multiplication.

$$\frac{\sqrt{3}\times 2}{1\times 2}=\frac{\sqrt{3}}{1}\times \frac{2}{2}$$

Dividing the same numbers.

$$\frac{\sqrt{3}}{1}\times \frac{2}{2}=\frac{\sqrt{3}}{1}\times 1$$

Multiplying a number by one, which does not change its value.

$$\frac{\sqrt{3}}{1}\times 1=\frac{\sqrt{3}}{1}$$

The fraction equals its numerator if its denominator is one.

$$\frac{\sqrt{3}}{1}=\sqrt{3}$$