sin30×sin60+cos30×cos60=

sin 30 = 1/2
sin 60 = 1/2√3
cos 30 = 1/2√3
cos 60 = 1/2

1/2 x 1/2√3 + 1/2 x 1/2√3 = √3/4 + √3/4 = 2√3/4

1/2×1/2/3+ 1/2×1/2/3 =/3/4 +/3/4=2/3/4