Question

If A + B+ C = 180 , Prove that cos 2A + cos 2B + cos 2C = 2+2 sinA sinB sinC

Answer 1

Step-by-step explanation:

now squaring on both side .

then ,(CosA×CosB+CosC)^2=sin^2A×sin^2B

=Cos^2A×Cos^2B+2CosA×CosB×CosC=(1-Cos^A)*(1-Cos^2B)

=Cos^2A×Cos^2B+2CosA×CosB×CosC+cos^2C=1-Cos^2B+Cos^2A-Cos^2A×Cos^2B

=Cos^2A+cos^2B+Cos^2C=1-2cosAcosBcosC

=hope it help you.