How do you express sin(π6)cos(9π8) without using products of trigonometric functions?

2 Answers
Mar 25, 2016

=1212(1+12)

Explanation:

sin(π6)cos(π+π8)=12cos(π8)
=1212(1+cos(π4))=1212(1+12)

It may also be expressed as sum of two trigonometric functions
using formula
sinAcosB=12(sin(A+B)+sin(AB))

sin(π6)cos(π+π8)=sin(π6)cos(π8)

=12(sin(π6+π8)+sin(π6π8))

=12(sin(7π24)+sin(π24)

Mar 25, 2016

(12)(cosπ8)

Explanation:

P=sin(π6).cos(9π8)
Trig table --> sin(π6)=12
cos(9π8)=cos(π8+π)=cos(π8)
The product P can be expressed as:
P=(12)(cosπ8)

If being asked, we can find P by evaluating cos(π8), using the trig identity: cos2a=2cos2a1.