# Prove that (tanx)(sin2x) = 2 – 2cos^2

Prove that
$\left(\mathrm{tan}x\right)\left(\mathrm{sin}2x\right)=2–2{\mathrm{cos}}^{2}$
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Cullen
$LHS=\left(\mathrm{tan}x\right)\left(\mathrm{sin}2x\right)$
$=\left(\frac{\mathrm{sin}x}{\mathrm{cos}x}\right)\left(2\mathrm{sin}x.\mathrm{cos}x\right)$
$=2{\mathrm{sin}}^{2}x=2\left(1-{\mathrm{cos}}^{2}x\right)$
$=2-2{\mathrm{cos}}^{2}x=RHS$