use trigonometric identities to find the exact value. tan 35[]+tan 115[] over 1-tan 35[]tan 115[]?

Question

1. -sqrt[]3
2. -2
3. -1/2
4. -sqrt[]3/3

Answer 1

Use the trig identity:
tan(u +/- v) = (tanu +/- tanv)/(1 -/+ tanu tanv)
(tan35 + tan115)/(1 - tan35 tan115) = tan(35 + 115) = tan150 = -1/√3 =-(√3)/3 The correct answer is 4.