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# Identity question help?

(sin(x)*cos(x)-sin(x)) / (sin(x)+cos(x)) = sin(x)-cos(x)

prove the identity

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- morganLv 77 years agoFavorite Answer
Given:

(sin(x)*cos(x)-sin(x)) / (sin(x)+cos(x)) = sin(x)-cos(x)

This is not an identity. To prove that, I simply need

to show a single counter example -- for example x = 0.

(sin(x)*cos(x)-sin(x)) / (sin(x)+cos(x)) = sin(x)-cos(x)

(sin(0)*cos(0)-sin(0)) / (sin(0)+cos(0)) = sin(0)-cos(0)

(0*1-0) / (0+1) = 0-1

(0) / (1) = -1

0 = -1

Since this is false, the given "identity" is not true.

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