How do you express sin(π12)cos(π4) without products of trigonometric functions?

1 Answer
Jun 19, 2016

(24)23

Explanation:

P=sin(π12).cos(π4)
Trig table --> cos(π4)=22.
Then P can be expressed as: P=(22)sin(π12)
We can evaluate sin(π12), using the trig identity:
cos2a=12sin2a
cos(π6)=32=12sin2(π12)
2sin2(π12)=132=232
sin2(π12)=234
sin(π12)=±232
Take the positive value because sinπ12 is positive
Finally,
P=(24).23