Find the exact value of the expression Sin pi3 cos 5 pi12 c
Find the exact value of the expression Sin pi/3 cos 5 pi/12 + cos pi/3 sin 5 pi/12 Sin pi/3 cos 5 pi/12 + cos pi/3 sin 5 pi/12 = (Simplify your answer, including any radicals Use integers or fractions for any
Solution
sinAcosB+cosAsinB=sin(A+B)
sin(/3)cos(5/12)+cos(/3)sin(5/12)=sin(/3+5/12)
sin(/3)cos(5/12)+cos(/3)sin(5/12)=sin(4/12+5/12)
sin(/3)cos(5/12)+cos(/3)sin(5/12)=sin(9/12)
sin(/3)cos(5/12)+cos(/3)sin(5/12)=sin(3/4)
sin(/3)cos(5/12)+cos(/3)sin(5/12)= 1/2
