Question

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

Trigonometric equation and identitie

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

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: $$-1$$