Write the expression as the sine, cosine, or tngent of a single angle.

Question

(tan(4pi/5)-tan(2pi/15))/(1+tan(4pi/5)tan(2pi/15))

Answer 1

tan(A − B) = (tan A − tan B)/(1 + tan A tan B) so it equals

 

tan (4pi/5 - 2pi/15) = tan (12pi/15 - 2pi/15) = tan (10pi/15) = tan (2pi/3)