How do you express sin(π6)cos(5π12) without using products of trigonometric functions?

1 Answer
Jan 25, 2016

(14)(23)

Explanation:

a. Find sin (pi/6).
Trig Table of special arcs --> sinπ6=12
b. Find cos (5pi)/2
cos(10π)12=cos(5π6)=32
Use trig identity: cos2x=2cos2x1
cos(5π6)=32=2cos2(5π12)1
2cos2(5π12)=132=232
cos(5π12)=232
Finally,
sinπ6.cos(5π12)=(14)(23)