How do you express cos(π3)sin(π8) without using products of trigonometric functions?

1 Answer
Jul 11, 2016

P=(14)22

Explanation:

P=cos(π3).sin(π8)
Trig table --> cos (pi/3) = 1/2.
There for, P can be expressed as P=(12)sin(π8)
We can evaluate sin (pi/8) by using trig identity:
cos 2a = 1 - 2sin^2 a
cos(2π)8=cos(π4)=22=12sin2(π8)
2sin2(π8)=122=222
sin2(π8)=224
sin(π8)=±222
Since sin(π8) is positive, then,
P=(14)22