Question

cosA+cosB+cosC=-1-4cosA+cosBcosC​

Answer 1

Step-by-step explanation:

LHS

= ( cos 2A + cos 2B ) + cos 2C

= [ 2 cos (A+B) cos (A-B) ] + cos 2C

= [ 2 cos (π-C) cos (A-B) ] + ( 2 cos² C - 1 )

= [ 2( -cos C ) cos (A-B) ] + 2 cos² C - 1

= -1 - 2 cos C cos (A-B) + 2 cos² C

= -1 - 2 cos C [ cos (A-B) - cos C ]

= -1 - 2 cos C [ cos (A-B) - ( -cos (A+B)) ]

= -1 - 2 cos C [ cos (A+B) + cos (A-B) ]

= -1 - 2 cos C [ 2 cos A cos B ]

= -1 - 4 cos A cos B cos C

= RHS