This requires intermediate algebra skills.
We are simply stating this in another way:
#(sin5pi)/12 = sin (π/4 + π/6)#
Using an identity (#cos (a + b) = cos a cos b - sin a sin b#) to represent this so that we can use more to simplify them afterwards:
#cos(pi/6 + pi/4) =(cospi/4)( cos pi/6) + (sinpi/4)( sin pi/6) #
Now we can simply substitute the values we memorized to this:
#= (sqrt3 / 2) ( sqrt2 / 2) - (1/2) (sqrt2 / 2)#
Therefore, we can state that:
#=sqrt6 / 4 - sqrt2 / 4#
Thus,
#:. (sqrt6 - sqrt2) / 4#
Hope this helped :)!
