How do I show this equation is not an identity in paragraph form? sin α=square root 1-cos²α

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Answer 1 · 2018-03-23T23:29:42

Can't really do that, because this is a true statement

Using the identity:
${sin}^{2} α + {cos}^{2} α = 1$ $sin^2alpha+cos^2alpha=1$

Start:

$sin α = \sqrt{1 - {cos}^{2} α}$ $sinalpha= sqrt(1-cos^2alpha)$

$sin α = \sqrt{({sin}^{2} α + {cos}^{2} α) - {cos}^{2} α}$ $sinalpha= sqrt((sin^2alpha+cos^2alpha)-cos^2alpha)$

$sinalpha= sqrt(sin^2alphacancel(+cos^2alpha)cancel(-cos^2alpha))$

$sinalpha= sqrt(sin^2alpha)$

$sinalpha= sinalpha$