# Solve (sin x + cos x)(sin x + cos x)

Solve $\left(\mathrm{sin}x+\mathrm{cos}x\right)\left(\mathrm{sin}x+\mathrm{cos}x\right)$
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smallq9
Use Distributive Property of FOIL method to obtain:
${\mathrm{sin}}^{2}x+2\mathrm{sin}x\mathrm{cos}x+{\mathrm{cos}}^{2}x$
Use the identity: ${\mathrm{sin}}^{2}x+{\mathrm{cos}}^{2}x=1$
$=1+2\mathrm{sin}x\mathrm{cos}x$
Use the double-angle identity: ${\mathrm{sin}}^{2}x=2\mathrm{sin}x\mathrm{cos}x$
$=1+\mathrm{sin}2x$