Oberlaudacu

2022-01-15

Simplifying $\frac{{\mathrm{cos}}^{2}x-{\mathrm{sin}}^{2}x}{\mathrm{sin}2x}$

Edward Patten

${\mathrm{cos}}^{2}x-{\mathrm{sin}}^{2}x=\mathrm{cos}\left(2x\right)$ . So the result can be written as $\mathrm{cot}\left(2x\right)$

sonSnubsreose6v

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$\frac{\mathrm{cos}x}{2\mathrm{sin}x}-\frac{\mathrm{sin}x}{2\mathrm{cos}x}=\frac{1}{2\mathrm{tan}x}-\frac{12}{\mathrm{tan}x}=\frac{1-{\mathrm{tan}}^{2}x}{2\mathrm{tan}x}=\frac{1}{\mathrm{tan}2x}$

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