How do you express sin(π8)cos((5π12) without using products of trigonometric functions?

1 Answer
Feb 9, 2016

(22).(2+3)4

Explanation:

Product P=sin(π8).cos(5π12).
a. Find sin(π8) by trig identity: cos2x=12sin2x
cos(π4)=22=12sin2(π8)
sin2(π8)=224
sin(π8)=222 --> (sin π8 is positive)
b. Find cos(5π12)=cost by identity: cos2t=2cos2t1
cos2t=cos(10π12)=cos(5π6)=32
32=2cos2t1
2cos2t=1+32=2+32
cos2t=2+34
cost=cos(5π12)=2+32--> (cos t is positive)

Finally: P=(22).(2+3)4