Question

How do you express `sin(pi/ 4 ) * sin( ( 7 pi) / 12 )` without using products of trigonometric functions?

Answer 1

`1/2 [cos (pi/3) - cos ((5pi)/6)]`

Explanation:

Use trignometrical identity cos(A-B) -cos (A+B)= 2 sin A sin B.

`sin pi/4 .sin (7pi)/12= 1/2 [ cos ((7pi)/12- pi/4)- cos ((7pi)/12 + pi/4)]`

=`1/2 [cos (pi/3) - cos ((5pi)/6)]`