Hitunglah nilai daru tan 105 derajat

[tex]\tan{105}=\tan{180-75}=-\tan{75}[/tex]
[tex]\tan{75}=-\tan{(45+30)}=-\frac{\tan{45}+\tan{30}}{1-\tan{45}\tan{30}}=-\frac{1+\frac{\sqrt{3}}{3}}{1-1*\frac{\sqrt{3}}{3}}=-\frac{\frac{3+\sqrt{3}}{\sqrt{3}}}{\frac{3-\sqrt{3}}{\sqrt{3}}}=-\frac{3+\sqrt{3}}{3-\sqrt{3}}[/tex]

[tex]-\frac{3+\sqrt{3}}{3-\sqrt{3}}*\frac{3+\sqrt{3}}{3+\sqrt{3}}=-\frac{(3+\sqrt{3})^{2}}{(3-\sqrt{3})(3+\sqrt{3})}=-\frac{3^{2}+2*3*\sqrt{3}+(\sqrt{3})^{2}}{3^{2}+3\sqrt{3}-3\sqrt{3}-(\sqrt{3})^{2}}=-frac\{9+6\sqrt{3}+3}{9-3}=-\frac{12+6\sqrt{3}}{6}=-(2+\sqrt{3})[/tex]
waitt sorry kalo typo

Rumus

tan 105° = tan (60° + 45°)

tan 60° + tan 45° = -----------1 - [tan 60° . tan 45°]

√3 + 1= ---------------1 - [√3][1]
√3 + 1= ----------- ..............

Rasionalkan
1 - √31 + √3
1 + √3= ----------- x ---------1 - √3
1 + √31 + 2√3 + 3= ------------------
1 - 34 + 2√3= --------------- 2

∴ tan 105° = - 2 - √3