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

1 Answer
Feb 17, 2017

2+24

Explanation:

P=sin(π6).cos(π8)
Trig table gives --> sin (pi/6) = 1/2
P=(12)cos(π8).
We can evaluate cos(π8) by using trig identity:
2cos2a=1+cos2a
In this case:
2cos2(π8)=1+cos(π4)=1+22=2+22
cos2(π8)=2+24
cos(π8)=±2+22.
Since cos(π8) is positive, take the positive answer.
Finally,
P=(12)cos(π8)=2+24