Question 978087


 Use the formula,

{{{cos (A + B) = (cos (A)*cos( B)) - (sin(A)*sin (B))


{{{cos (105) = cos (90 + 15)}}}

{{{cos (90 + 15) = (cos (90)*cos (15)) - (sin (90)*sin (15))}}}

Since {{{cos( 90) = 0}}} and {{{sin (90) = 1}}}, we have

{{{cos (90 + 15) = (0 * cos (15)) - (1 * sin (15))}}}

{{{cos (90 + 15) = -sin( 15)}}}


 {{{-sin (15)=  -(sqrt(3)-1)/(2*sqrt(2))}}} or {{{(1-sqrt(3))/(2*sqrt(2))}}}