How do you express sin(π8)cos((5π4) without using products of trigonometric functions?

2 Answers
May 21, 2016

(22)sin(π8)

Explanation:

P=sin(π8).cos(5π4)
Trig table and property of supplementary arcs -->
cos(5π4)=cos(π4+π)=cos(π4)=22.
Therefor, P can be expressed as
P=(22)sin(π8)

Note. We can evaluate P by finding exact value of sin (pi/8), using the trig identity:
cos(π4)=22=12sin2(π8)

May 21, 2016

sin(π8)cos(5π4)=14422

Explanation:

sin(π8)cos(5π4)

Let us first calculate

cos(5π4)=cos(π4+π)=cos(π4)=12

For sin(π8), let us use the identity cos2θ=12sin2θ

Hence, cos(π4)=12sin2(π8) or

12=12sin2(π8) or

2sin2(π8)=112=122=222

or sin2(π8)=224

or sin(π8)=1222

Hence, sin(π8)cos(5π4)=1222×22

or sin(π8)cos(5π4)=14422