How do you express sin(π6)cos(15π12) without using products of trigonometric functions?

2 Answers
Mar 26, 2016

24

Explanation:

P=sin(π6)cos(15π12).
Trig table --> sinπ6=12
cos(15π12)=cos(9π12+2π)=cos(3π4)=
=cos(3π4)=22.
P=(12)(22)=24

Apr 4, 2016

sin(π6)cos(15π12)=12sin(17π12)12sin(13π12)

Explanation:

2sinAcosB=sin(A+B)+sin(AB)
sinAcosB=12(sin(A+B)+sin(AB))
A=π6,B=15π12
sin(π6)cos(15π12)=12(sin(π6+15π12)+sin(π615π12))
=12(sin(17π12)+sin(13π12))
=12sin(17π12)12sin(13π12)