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Find the exact value of tan 106 + tan(-61)/ 1- tan 106 tan (-61)

Find the exact value of tan 106 + tan(-61)/ 1- tan 106 tan (-61)-example-1
User Samer
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Answer

1

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}

User Oskob
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