Question

find the exact value: sin (105 degrees) cos (15 degrees). Somebody explain me the steps please? Medal to helper.

Answer 1

look first we should split the (105) into a familiar angles (90 , 45 , 30 ,60 ,etc...)
so since 105 = 45 + 60
then sin(105)=sin(45+60)
and the same with the cosine.
then solve it as any sum of 2 angles ;)

Answer 2

but look out for the angle (15)
you should use "the equation of the half of the angle" : \[\cos(\frac{ x }{ 2 }) = \sqrt{\frac{ 1+cosx }{ 2 }}\]