Question

How do you express `sin(pi/ 4 ) * sin( ( 5 pi) / 6 )` without using products of trigonometric functions?

Answer 1

see below

Explanation:

Use formula: `-2sinAsinB=cos(A+B)-cos(A-B)`

`sin (pi/4) sin ((5pi)/6)=-1/2[cos(pi/4+(5pi)/6)-cos(pi/4-(5pi)/6)]`

`=-1/2 [cos((13pi)/12)-cos(-(7pi)/12)]`

`=-1/2 [cos((13pi)/12)-cos((7pi)/12)]`

`=-1/2 cos((13pi)/12)+1/2 cos((7pi)/12)`