How do you express sin(π6)cos(3π8) without using products of trigonometric functions?

1 Answer
Mar 17, 2016

224

Explanation:

P=sin(π6).cos(3π8).
Trig table --> sinπ6=12
Find cos(3π8) by the identity: cos2a=2cos2a1
cos(6π8)=2cos2(3π8)1.
cos(3π4)=22=2cos2(3π8)1
2cos2(3π8)=122=222
cos2(3π8)=224
cos(3π8)=222 (since cos(3π8) is positive.
Finally,

P=(12)(222)=(224)