Evaluate this integral ${\int}_{0}^{\frac{\pi}{4}}\frac{\mathrm{cos}2x}{\mathrm{cos}x+\mathrm{sin}x}dx$

Francisca Rodden
2022-01-17
Answered

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

Answered 2022-01-18
Author has **37** answers

Hint: Notice, that:

${\int}_{0}^{\frac{\pi}{4}}\frac{{\mathrm{cos}}^{2}x-{\mathrm{sin}}^{2}x}{\mathrm{cos}x+\mathrm{sin}x}dx=$

$={\int}_{0}^{\frac{\pi}{4}}\frac{(\mathrm{cos}x-\mathrm{sin}x)(\mathrm{cos}x+\mathrm{sin}x)}{\mathrm{cos}x+\mathrm{sin}x}dx=$

$={\int}_{0}^{\frac{\pi}{4}}(\mathrm{cos}x-\mathrm{sin}x)dx$

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