Determine if the following is an identity.
-$$\cos ^ { 2 } x - \sin ^ { 2 } x = 1 - 2 \sin ^ { 2 } x$$
A) Not an identity
B) Identity

Question

Quizplus · Accepted Answer

This is an identity because it can be derived from the Pythagorean identity $\cos^2x + \sin^2x = 1$. Subtracting $\sin^2x$ from both sides gives $\cos^2x = 1 - \sin^2x$, and further substituting $1 - \sin^2x$ with $1 - 2\sin^2x + \sin^2x$ results in the given equation, proving it's an identity.

Determine If the Following Is an Identity cos⁡2x−sin⁡2x=1−2sin⁡2x\cos ^ { 2 } x - \sin ^ { 2 } x = 1 - 2 \sin ^ { 2 } xcos2x−sin2x=1−2sin2x

Determine If the Following Is an Identity $\cos ^ { 2 } x - \sin ^ { 2 } x = 1 - 2 \sin ^ { 2 } x$