How do you express cos(4π3)cos(π6) without using products of trigonometric functions?

2 Answers
Apr 1, 2016

32

Explanation:

P=cos(4π3).cos(π6)
Trig table --> cos(π6)=32
cos(4π3)=cos(π3+3π3)=cos(π3+π)=cos(π3)=12
P=(12)(32)=34

Apr 4, 2016

cos(4π3)cos(π6)=12cos(9π6)+12cos(7π6)=34

Explanation:

2cosAcosB=cos(A+B)+cos(AB)
cosAcosB=12(cos(A+B)+cos(AB))
A=4π3,B=π6
cos(4π3)cos(π6)=12(cos(4π3+π6)+cos(4π3π6))
=12(cos(9π6)+cos(7π6))
=12cos(9π6)+12cos(7π6)
=12(0)+12(32)
=34
cos(4π3)cos(π6)=12cos(9π6)+12cos(7π6)=34