If A+B+C = 180 then prove that cos^2A + cos^2B - cos^2C = 1 - 2 sinA sinB sinC Share with your friends Share 9 Ajanta Trivedi answered this given: A+B+C=180 .............(1) LHS of the given equation: cos2A+cos2B-cos2C=12.2cos2A+2cos2B-2cos2C=12.1+cos2A+1+cos2B-2cos2C [since cos2θ=2cos2θ-1=12.2+cos2A+cos2B-2cos2C=12.2+2cos(A+B).cos(A-B)-2cos2C [since cosC+cosD=2cosC+D2.cosC-D2 =12.2+2cos(180-C).cos(A-B)-2cos2C=12.2-2cosC.cos(A-B)-2cos2C=1-cosC.cos(A-B)+cosC=1-cosC.cos(A-B)-cos(A+B) [from eq(1)=1-cosC.2sinA.sinB=1-2sinAsinB.cosC=RHS hope this helps you 5 View Full Answer
