# Evaluate this integral \int_0^{\frac{\pi}{4}} \frac{\cos 2x}{\cos x+\sin x}dx

Evaluate this integral ${\int }_{0}^{\frac{\pi }{4}}\frac{\mathrm{cos}2x}{\mathrm{cos}x+\mathrm{sin}x}dx$
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Kayla Kline
Hint: Notice, that:
${\int }_{0}^{\frac{\pi }{4}}\frac{{\mathrm{cos}}^{2}x-{\mathrm{sin}}^{2}x}{\mathrm{cos}x+\mathrm{sin}x}dx=$
$={\int }_{0}^{\frac{\pi }{4}}\frac{\left(\mathrm{cos}x-\mathrm{sin}x\right)\left(\mathrm{cos}x+\mathrm{sin}x\right)}{\mathrm{cos}x+\mathrm{sin}x}dx=$
$={\int }_{0}^{\frac{\pi }{4}}\left(\mathrm{cos}x-\mathrm{sin}x\right)dx$