Answer:
The answer is the last one
[tex]tan(x_{1}+x_{2}+x_{3})=\frac{tanx_{1}+tan(x_{2}+x_{3})}{1-tanx_{1}tan(x_{2}+x_{3})}[/tex]
Step-by-step explanation:
∵ [tex]tan(x_{1}+x_{2}+x_{3}=\frac{tanx_{1}+tan(x_{2}+x_{3})}{1-tanx_{1}tan(x_{2}+x_{3})}[/tex]
[tex]=\frac{tanx_{1}+\frac{tanx_{2}+tanx_{3}}{1-tanx_{2}tanx_{3}} }{1-tanx_{1}(\frac{tanx_{2}+tanx_{3}}{1-tanx_{2}tanx_{3}})}[/tex]
Multiply up and down by [tex]1-tanx_{2}tanx_{3}[/tex]
[tex]\frac{tanx_{1}(1-tanx_{2}tanx_{3})+tanx_{2}+tanx_{3}}{1-tanx_{2}tanx_{3}-tanx_{1}tanx_{2}-tanx_{1}tanx_{3}}[/tex]
[tex]=\frac{tanx_{1}+tanx_{2}+tanx_{3}-tanx_{1}tanx_{2}tanx_{3}}{1-tanx_{1}tanx_{2}-tanx_{2}tanx_{3}-tanx_{1}tanx_{3}}[/tex]
