Question

Prove that (Cosx-Cos³x)/Sinx=SinxCosx​

Answer 1

Answer:

(Cosx-Cos³x)/Sinx=SinxCosx

Step-by-step explanation:

sin3x−cos3x

=sinxsin2x−cosxcos2x

=sinx(1−cos2x)−cosx(1−sin2x)

=sinx−sinxcos2x−cosx+cosxsin2x

=sinx−cosx+(sinx−cosx)sinxcosx  

=(sinx−cosx)(1+sinxcosx