How do you express sin(π4)sin(5π12) without using products of trigonometric functions?

1 Answer
Jun 24, 2016

(24)2+3

Explanation:

Product P=sin(π4).sin(5π12)
Trig table -->
sin(π4)=22
P can be expressed as:
(22).sin(5π12).
We can evaluate sin(5π12) by using the trig identity:
cos2a=12sin2a
cos(10π12)=cos(5π6)=32=12sin2(5π12)
2sin2(5π12=1+32=2+32
sin2(5π12)=2+34
sin(5π12)=2+32 (note: sin ((5pi)/12) is positive)
Finally,
P=(24)(2+3)