Question

Rewrite each expression as a single trigonometric ratio, and then evaluate the ratio ( show full work )

1a) tan 170• - tan 110• / 1+ tan 170• tan 110•

b) cos 5pie/12 x cos pie over 12 + sin 5pie over 12 x sin pie over 12

Answer 1

(tan(a) - tan(b))/(1+ tan(a)*tan(b)) = tan(a-b)

(tan(170^o) - tan(110^o))/(1+ tan(170^o)*tan(110^o)) = tan(170^o-110^o) = tan(60^o) = sin(60^o)/cos(60^o) = $\sqrt{3}$

cos(a)*cos(b) + sin(a)*sin(b) = cos(a-b)

cos(5$\pi$/12)*cos($\pi$/12) + sin(5$\pi$/12)*sin($\pi$/12) = cos(5$\pi$/12 - $\pi$/12) = cos(4$\pi$/12) = cos($\pi$/3) = 1/2