Question

prove that sin780°.sin480°+cos240°.cos300°=1/2​

Answer 1

sin780=sin(360+360+60)=sin60=√3/2

sin480=sin(360+90+30)=cos30=√3/2

cos240=cos(180+60)=-cos60=-1/2

cos300=cos(270+30)=sin30=1/2

so sin780×sin480+cos240×cos 300

√3²/2²+(-1)(1)/2²

3/4-1/4

2/4

1/2

hence proved