# Solve frac{csc x(sin^{2}x+cos^{2}xtan x)}{sin x+cos x}

Solve $\frac{\mathrm{csc}x\left(si{n}^{2}x+co{s}^{2}x\mathrm{tan}x\right)}{\mathrm{sin}x+\mathrm{cos}x}$
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Faiza Fuller
Write in terms of sine and cosine:
$=\frac{\left(\frac{1}{\mathrm{sin}x}\right)\left(si{n}^{2}x+co{s}^{2}x×\frac{\mathrm{sin}x}{\mathrm{cos}x}\right)}{\left(\mathrm{sin}x+\mathrm{cos}x\right)}$
Simplify:
$\frac{\left(1/\mathrm{sin}x\right)\left(si{n}^{2}x+\mathrm{cos}x\mathrm{sin}x\right)\right)}{\left(\mathrm{sin}x+\mathrm{cos}x\right)}$
Apply distributive property: a(b+c)=ab+c
$=\frac{\mathrm{sin}x+\mathrm{cos}x}{\mathrm{sin}x+\mathrm{cos}x}=1$