Question

Find the exact value of the expression. ( tan25^(circ) +tan110^(circ))/(1-tan25^(circ)*tan110^(circ))

Trigonometric equation and identitie
ANSWERED
asked 2021-03-06

Find the exact value of the expression.
\( \tan25^{\circ} + \tan 110^{\circ}/1-\tan25^{\circ} \cdot \tan110^{\circ}\)

Answers (1)

2021-03-07

40
use the identity:
\(\tan(u+v)=(\tan u+\tan v)/(1-\tan u \cdot \tan v)\)
where:
\(u=25^{\circ},v=110^{\circ}\)
Therefore,
\((\tan25^{\circ}+\tan110^{\circ})/(1+\tan25^{\circ} \cdot \tan110^{\circ})=\tan(25^{\circ}+110^{\circ})\)
\((\tan25^{\circ}+\tan110^{\circ})/(1+\tan25^{\circ} \cdot \tan110^{\circ})=(\tan135^{\circ})\)
\((\tan25^{\circ}+\tan110^{\circ})/(1+\tan25^{\circ} \cdot \tan110^{\circ})\)
Result: \(-1\)

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