Question

Prove that cos 2 76 +cos 2 16 - cos76.cos16 = 3/4

Answer 1

LHS=cos276°+cos216°−cos76° .cos16° =cos276°+(1−sin216°)− 1 2 (2cos76°.cos16°).....(1) now,weknowthat, cosC+cosD=2cos( C+D 2 )cos ( C−D 2 ) so,2cos76°.cos16°= [cos(76°+16°)+cos(76°−16°)] ⇒2cos76°.cos16°=cos92°+cos 60° Now,from(1),wehave, LHS=cos276°+(1−sin216°)− 1 2 (cos92°+cos60°) =(cos276°−sin216°)+1− 1 2 (cos92°+cos60°).......(2