নির্দিষ্ট যোগজ

0π4cos2θcos2θ=?\int_0^{\frac{\pi}{4}} \frac{cos 2 \theta}{cos² \theta} = ?

RU H 15-16

 0π/4cos2θcos2θdθ=0π/42cos2θ1cos2θdθ=0π/4(2sec2θ)dx=[2θtanθ]0π=2π4tanπ4(2.0tan0)=π21 \begin{array}{l}\text { } \int_{0}^{\pi / 4} \frac{\cos {2} \theta}{\cos ^{2} \theta} d \theta \\ =\int_{0}^{\pi / 4} \frac{2 \cos ^{2} \theta-1}{\cos ^{2} \theta} d \theta \\ =\int_{0}^{\pi / 4}\left(2-\sec ^{2} \theta\right) d x=[2 \theta-\tan \theta]_{0}^{\pi} \\ =2 \cdot \frac{\pi}{4}-\tan \frac{\pi}{4}-(2.0-\tan 0)=\frac{\pi}{2}-1\end{array}

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