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How do you verify ${(cos x - sin x)}^{2} + 2 sin x cos x = 1$ $(cosx - sinx) ^ 2 + 2 sinx cosx = 1$ ?

1 Answer

NostalGia · Stefan V.

Jun 22, 2018

Below.

Explanation:

$left side$ $"left side"$

$= {cos}^{2} x - 2 sin x cos x + {sin}^{2} x + 2 sin x cos x$ $= cos^2x - 2sinxcosx + sin^2x + 2sinxcosx$

$= {cos}^{2} x + {sin}^{2} x$ $= cos^2x + sin^2x$

$= 1$ $= 1$

$=$ $=$ $right side$ $"right side"$

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