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

1 Answer
Feb 26, 2016

234

Explanation:

On the unit circle, using property of complementary arcs:
cos(5π12)=sin(π2+5π12)=sin(11π12)=sinπ12
Product P=sin(π12).cos(5π12)=sin2(π12).
Find sin2(π12).
Use trig identity: cos(π6)=12sin2(π12)=32
2sin2(π12)=132=232
P=sin2(π12)=234