Question

prove that sin 780 x sin 480 + cos 120 x sin 30 =1/2​

Answer 1

sin(780) = sin(780 - 720) = sin(60) = (sqrt3)/2

sind(480) = sin(480 - 360) = sin(120) = sin(60) = (sqrt3)/2

cos(120) = - cos(60) = -1/2

sin(30) = 1/2 Therefore:

sin(780) sin(480) + cos(120) sin(30) =

[(sqrt3)/2][(sqrt3)/2] + [-1/2][1/2] = (3/4) - (1/4) = 2/4 = 1/2