Which of the following are identities? more than 1

a. sin x+ sin5x=tan3x
b. sin^6 x+cos^6 x=4-3sin^2 2x
c. cos^2 3x-sin^2 3x=cos6x
d.(sin x+ cos x)^2 =1+sin 2x

In order to confirm which of the given above is an identity, what we are going to do is to check them each. By definition, an identity is an equality relation A = B. 
After checking each options, the answers that are considered as identities would be options C and D. So here is how we proved it. Let's take option C.
cos^2(3x)-sin^2(3x)=cos(6x)
cos^2(3x)-sin^2(3x)=cos(2*3x)
cos^2(3x)-sin^2(3x)=cos(3x+3x)
cos^2(3x)-sin^2(3x)=cos(3x)cos(3x)-sin(3x)sin(3x)
cos^2(3x)-sin^2(3x)=cos^2(3x)-sin^2(3x)
So based on this, we can conclude that cos^2 3x-sin^2 3x=cos6x is an identity.
This is also the same process with option D.
Hope this answer helps.

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