How do you express cos(π3)sin(15π8) without using products of trigonometric functions?

1 Answer
Feb 25, 2016

P=12(2+22)

Explanation:

P=cos(π3).sin(15π8)
cos(π3)=12
sin(15π8)=sin(2ππ8)=sinπ8.
Find sin(π8) by using trig identity:
cos(π4)=2cos2(π8)1=22
2cos2(π8)=1+22=2+22
cos2(π8)2=2+24
cos(π8)=2+22 (cos (pi/8) is positive.)
P=122+22