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The value of the integral
$\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \log (\sec \theta-\tan \theta) \mathrm{d} \theta$ is
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$\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \log (\sec \theta-\tan \theta) \mathrm{d} \theta$ is
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\( 00 \)
Given that $I-\int_{-\pi / 4}^{\pi / 4} \log (\sec \theta-\tan \theta) d \theta-0$
Since, $\log (\sec \theta-\tan \theta)$ is an odd function and, if $f(\theta)=\log (\sec \theta-\tan \theta)$
then, $f(-\theta)=\log [\sec \theta+\tan \theta]$
$=-\log (\sec \theta-\tan \theta)=-f(\theta)$
Since, $\log (\sec \theta-\tan \theta)$ is an odd function and, if $f(\theta)=\log (\sec \theta-\tan \theta)$
then, $f(-\theta)=\log [\sec \theta+\tan \theta]$
$=-\log (\sec \theta-\tan \theta)=-f(\theta)$
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