In a quadrilateral ABCD if sin(A+B2)cos(A−B2)+sin(C+D2)cos(C−D2)=2 then ∑cosA2cosB2 is equal to
sinA+B2.cosA−B2+sinC+D2.cosC−D2=2 ⇒sinA+sinB+sinC+sinD=4 ⇒sinA=sinB=sinC=sinD=1 ⇒A=900=B=C=DNow ∑cosA2cosB2=6×(1√2)2=3
If A+B+C=180° , then prove that sinA+sinB+sinC = 4 cos(A/2) cos(B/2) cos(C/2)