 # Simplify the expression secx/sinx - sinx/cosx Globokim8 2020-11-01 Answered
Simplify the expression $\frac{\mathrm{sec}x}{\mathrm{sin}x}-\frac{\mathrm{sin}x}{\mathrm{cos}x}$
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$\mathrm{sec}x=\frac{1}{\mathrm{cos}x}$
$\frac{\frac{1}{\mathrm{cos}x}}{\mathrm{sin}x}-\frac{\mathrm{cos}x}{\mathrm{sin}x}$
$\frac{\frac{1}{\mathrm{cos}x}-\mathrm{cos}x}{\mathrm{sin}x}$
$\frac{\frac{1}{\mathrm{cos}x}-\frac{{\mathrm{cos}}^{2}x}{\mathrm{cos}x}}{\mathrm{sin}x}$
$\frac{1-\frac{{\mathrm{cos}}^{2}x}{\mathrm{cos}x}}{\mathrm{sin}x}$
${\mathrm{cos}}^{2}x+{\mathrm{sin}}^{2}x=1\to {\mathrm{sin}}^{2}x=1-{\mathrm{cos}}^{2}x$
$\frac{\frac{{\mathrm{sin}}^{2}x}{\mathrm{cos}x}}{\mathrm{sin}x}\to \left(\frac{{\mathrm{sin}}^{2}x}{\mathrm{cos}x}\right)•\left(\frac{1}{\mathrm{sin}x}\right)$
$=\frac{{\mathrm{sin}}^{2}x}{\mathrm{sin}x}\mathrm{cos}x$
$\frac{\mathrm{sin}x}{\mathrm{cos}x}=\mathrm{tan}x$
$=\mathrm{tan}x$