Question

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

Answer 1

`sinAsinB=-1/2 [cos(A+B)-cos(A-B)] =-> sin (pi/4)sin(pi/12)=-1/2[cos(pi/4 + pi/12)- cos(pi/4-pi/12)]=-1/2[cos(pi/3)-cos(pi/6)]=-1/2[1/2 -sqrt3/2]=-1/4+sqrt3/4=(sqrt3 -1)/4`

Explanation:

Use the sum and product formula and substitute in `pi/4` for A and `pi/12` for B then simplify as shown above.