Question

verify the identity : cos 3x = cos x( 1 -  4sin^2 x)

Answer 1

Remember Cos3x = 4Cos^3x-3Cosx

Sin^2x+Cos^x = 1

Left hand side identity = Cos3x

= 4Cos^3x-3Cosx

= Cosx(4Cos^2x-3)

= Cosx(4(1-Sin^2x)-3)

= Cosx(4-4Sin^2x-3)

= Cosx(1-4Sin^2x)

= Right hand side identity.