Question 151157
{{{sin(75)}}} Start with the given expression.



{{{sin(45+30)}}} Rewrite 75 as 45+30. Take note that 45 and 30 are angles found on the unit circle.



{{{sin(45)cos(30)+cos(45)sin(30)}}} Expand the expression using the Sum-Difference identity




{{{(sqrt(2)/2)(sqrt(3)/2)+(sqrt(2)/2)(1/2)}}} Evaluate {{{sin(45)}}} to get {{{sqrt(2)/2}}}. Evaluate {{{cos(30)}}} to get {{{sqrt(3)/2}}}. Evaluate {{{cos(45)}}} to get {{{sqrt(2)/2}}}. Evaluate {{{sin(30)}}} to get {{{1/2}}}




{{{sqrt(6)/4+sqrt(2)/4}}} Multiply



{{{(sqrt(6)+sqrt(2))/4}}} Add the fractions.



So {{{sin(75)=(sqrt(6)+sqrt(2))/4}}}