Answer
1
Step-by-step explanation
Given the expression:
[tex]\frac{\tan(106\degree)+\tan(-61\degree)}{1-\tan(106\degree)\cdot\tan(-61\degree)}[/tex]
It has the form:
[tex]\tan(a+b)=\frac{\tan(a)+\tan(b)}{1-\tan(a)\cdot\tan(b)}[/tex]
with a = 106° and b = -61°. Therefore, the first expression is equivalent to:
[tex]\begin{gathered} \frac{\tan(106\operatorname{\degree})+\tan(-61\operatorname{\degree})}{1-\tan(106\operatorname{\degree})\tan(-61\operatorname{\degree})}=\tan(106\degree-61\operatorname{\degree}) \\ \frac{\tan(106\operatorname{\degree})+\tan(-61\operatorname{\degree})}{1-\tan(106\operatorname{\degree})\tan(-61\operatorname{\degree})}=\tan(45\operatorname{\degree}) \\ \frac{\tan(106\operatorname{\degree})+\tan(-61\operatorname{\degree})}{1-\tan(106\operatorname{\degree})\tan(-61\operatorname{\degree})}=1 \end{gathered}[/tex]
