Tentukan nilai tan 195 - tan 165

[tex]
\text{Pertama, perhatikan bahwa}\\
\tan{15\degree}\\
=\tan{(60\degree-45\degree)}\\
=\frac{\tan{60\degree}-\tan{45\degree}}{1+\tan{60\degree}\tan{45\degree}}\\
=\frac{\sqrt{3}-1}{1+\sqrt{3}\cdot1}\\
=\frac{\sqrt{3}-1}{\sqrt{3}+1}\\
\\
\text{Selanjutnya, perhatikan bahwa}\\
\tan{195\degree}-\tan{165\degree}\\
=\tan{(180\degree+15\degree)}-\tan{(180\degree-15\degree)}\\
=\tan{15\degree}-\left(-\tan{15\degree}\right)\\
=2\tan{15\degree}\\
=2\cdot\frac{\sqrt{3}-1}{\sqrt{3}+1}
[/tex]