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

1 Answer
Dec 31, 2016

(22)(222)

Explanation:

P=sin(π8).cos(π4)
Trig table gives cos(π4)=22, then P can be expressed as:
P=(22)sin(π8).
We can evaluate sin(π8) by applying the trig identity:
2sin2a1cos2a
2sin2(π8)=1cos(π4)=122=222
sin2(π8)=224
sin(π8)=±(222)
Since sin(π8) is positive, take the positive value.
Finally:
P=(22)(222)