Use a sum or difference formula to find the exact value of t

Use a sum or difference formula to find the exact value of the trigonometric function. sin 105Degree sin 105Degree = (Simplify your answer. including any radical* Use integers or fractions for any number* in the expression.)

Solution

sin(105⁰)

=sin(60⁰+45⁰)

sin(a+b)=sin(a)cos(b) +cos(a)sin(b)

=sin(60⁰)cos(45⁰) +cos(60⁰)sin(45⁰)

=(3 /2)(1/2) +(1/2)(1/2)

=(3 +1)/(22)

=2(3 +1)/4