`(tan(140) - tan(60))/(1 + tan(140)tan(60))` Write the expression as a sine, cosine, or tangent of an angle.

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to recognize the formula `tan(a-b) = (tan a - tan b)/(1+ tan a*tan b). ` You need to put `a = 140^o` and `b = 60^o` , such that:

`tan(140^o - 60^o) = (tan140^o - tan 60^o)/(1 + tan 140^o*tan 60^o)`

`tan 80^o = (tan140^o - tan 60^o)/(1 + tan 140^o*tan 60^o)`

Hence, the given expression could be evaluated as the tangent of the difference of anglesĀ `140^o` and `60^o` , such that `(tan140^o - tan 60^o)/(1 + tan 140^o*tan 60^o) = tan 80^o.`