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Oskob · Answer 1 · 2023-07-12T20:05:06+0000

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Explanation

Given the expression:

$(\tan(106\degree)+\tan(-61\degree))/(1-\tan(106\degree)\cdot\tan(-61\degree))$

It has the form:

$\tan(a+b)=(\tan(a)+\tan(b))/(1-\tan(a)\cdot\tan(b))$

with a = 106° and b = -61°. Therefore, the first expression is equivalent to:

$\begin{gathered} \frac{\tan(106\operatorname{\degree})+\tan(-61\operatorname{\degree})}{1-\tan(106\operatorname{\degree})\tan(-61\operatorname{\degree})}=\tan(106\degree-61\operatorname{\degree}) \\ \frac{\tan(106\operatorname{\degree})+\tan(-61\operatorname{\degree})}{1-\tan(106\operatorname{\degree})\tan(-61\operatorname{\degree})}=\tan(45\operatorname{\degree}) \\ \frac{\tan(106\operatorname{\degree})+\tan(-61\operatorname{\degree})}{1-\tan(106\operatorname{\degree})\tan(-61\operatorname{\degree})}=1 \end{gathered}$

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