Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Prove the following:

cos 4 straight x space equals space 1 minus 8 sin squared straight x space cos squared straight x

Answer

Using  cos space 2 straight A space equals space 1 minus 2 sin squared straight A comma space we space get
L.H.S. = cos 4 straight x space equals space 1 minus 2 sin squared 2 straight x
         equals 1 minus 2 left parenthesis 2 sinx space cosx right parenthesis squared
         = 1 minus 2 left parenthesis 4 sin squared straight x space cos squared straight x right parenthesis
         = 1 minus 8 sin squared straight x space cos squared straight x
          = R.H.S.
Hence,        space space cos 4 straight x space equals space 1 minus space 8 space sin squared straight x space cos squared straight x

More Chapters from Principle of Mathematical Induction