Prove the following identity cos4 x sin4 x cos 2x We begin b

Prove the following identity. cos4 x sin4 x cos 2x We begin by factoring the left side of the equation. We can then use a Pyt hagorean Identity and a Doul 1 1)(cos2 x-sin2x). cos4 x-sin#x = ( cos2 x + cos2 x-sin2 x) = cos 2x

Solution

cos^4 x - sin^4 x = cos 2x

manipulating left hand side

cos^4 x - sin^4 x = ( cos^2 x + sin^2 x ) ( cos^2 x - sin^2 x )

= ( 1 ) (cos^2 x - sin^2 x )

= cos 2x

first blank = ( cos^2 x + sin^2 x )

second blank = 1