How do you express sin(π8)cos(7π6) without using products of trigonometric functions?

1 Answer
Jan 24, 2016

(3)(224)

Explanation:

First, find sin(π8) and cos(7π6) separately.
Call sin(π8)=sint
Use the trig identity: cos(2t)=12sin2t
cos(π4)=22=1sin2t
2sin2t=12=222
sin2t=224
sin(π8)=sint=222

cos(7π6)=cos(π6+π)=cos(π6)=32

Finally, sin(π8).cos(7π6)=(3)(224)