Differentiate and simplify: f(x)=sin^2(2x)-cos^2(2x)

[ttpp1124]

Homework Statement

Has this been simplified fully?

Relevant Equations

n/a

 

[Mark44]

Homework Statement:: Has this been simplified fully?
Relevant Equations:: n/a

View attachment 262618

Do you have a question here?

 

[benorin]

yes

 

[BvU]

Is that an answer to the quesion in post #1 or the one in post #2 ? Or both ?

Let me ask @ttpp1124 : do you expect there exists a simpler expression ? In what way ?

 

[benorin]

yes, it is fully simplified, and of course with trig you could go in many circles with identities but I believe the one stopped at is simplest.

 

[ttpp1124]

Do you have a question here?

yes, sorry, I forgot to include the question! here it is:

 

[pasmith]

I would use $\cos (2\theta) = \cos^2 \theta - \sin^2\theta$, from which immediately $y = -\cos(4x)$.

 

[BvU]

yes, sorry, I forgot to include the question! here it is:

Not much of a question !

Kudos @pasmith : the simplest path to the simplest result !