uplakanimkk

2022-07-07

Need help with a trigonometry proof: $\mathrm{sin}\left(90-\theta \right)=\mathrm{cos}\theta$

SweallySnicles3

Expert

You can use the formula $\mathrm{sin}\left(A-B\right)=\mathrm{sin}A\cdot \mathrm{cos}B-\mathrm{cos}A\cdot \mathrm{sin}B,$, so
$\mathrm{sin}\left(90-\theta \right)=\mathrm{sin}90\mathrm{cos}\theta -\mathrm{cos}90\mathrm{sin}\theta \phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}\mathrm{cos}\theta .$

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