Question

Show that sin780*sin480+cos240*cos300=1/2

Answer 1

)sin780.sin120+cos240.sin390 
=sin(8x90+60).sin(90+30) +cos(3x90-30).sin(4x90+30) 
=sin60.cos30+[-sin30].sin30 
=sin60.cos30 - sin30.sin30 
=(root3)/2 x (root3)/2 -1/2 x1/2 
=3/4 -1/4 
=2/4 
=1/2(proved)