How do you prove the identity (sin4)x(cos4)x?

1 Answer
Sep 3, 2015

You probably mean this one:

sin4xcos4x=cos2x

Explanation:

sin4xcos4x

=(sin2x)2(cos2x)2

=(sin2xcos2x)(sin2x+cos2x)

...using the difference of squares identity:

a2b2=(ab)(a+b)

Now sin2x+cos2x=1, so

(sin2xcos2x)(sin2x+cos2x)

=sin2xcos2x

=(cos2xsin2x)

=cos2x

...using the double angle formula for cos