Question

Verify sin4x-sin²x=cos4x-cos²x is an identity.
the 4 is supposed to be small like the 2

Answer 1

Answer:

It's an identity

Step-by-step explanation:

$\sin^4x-\sin^2x=\cos^4x-\cos^2x\\\\Ls=\sin^2x(\sin^2x-1)=-\sin^2x(1-\sin^2x)=-\sin^2x\cos^2x\\\\Rs=\cos^2x(\cos^2x-1)=-\cos^2x(1-\cos^2x)=-\cos^2x\sin^2x\\\\Ls=Rs\\\\\text{used}\\\\a^n\cdot a^m=a^{n+m}\\\\\text{distributive property}\ a(b+c)=ab+ac\\\\\sin^2x+\cos^2x=1\to \sin^2x=1-\cos^2x\\\\\sin^2x+\cos^2x=1\to \cos^2x=1-\sin^2x}$