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

Name: Determine if the following is an identity. -\[( \sin x + \cos x ) ^ { 2 } = 1\] A) Identity B) Not an identity
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Question

Quizplus · Accepted Answer

Expanding the left side gives $\sin^2x + 2\sin x\cos x + \cos^2x$, which simplifies to $1 + 2\sin x\cos x$ using the Pythagorean identity $\sin^2x + \cos^2x = 1$. This is not equal to 1 for all values of $x$, thus it is not an identity.

Determine If the Following Is an Identity (sin⁡x+cos⁡x)2=1( \sin x + \cos x ) ^ { 2 } = 1(sinx+cosx)2=1

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