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$\int \frac{d t}{a^{2} \sin^{2} t + b^{2} \cos^{2} t} is equal to$

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1atan−1atantb+k

−1abtan−1batant+c

1abtan−1batant+k

1abtan−1abtant+k

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detailed solution

Correct option is D

∫1a2sin2t+b2cos2tdt=∫1a2cos2tdttan2t+b2a2=1a2∫sec2⁡tdttan2⁡t+ba2 Put tan⁡t=rsec2tdt=dr Use ∫1a2+x2dx=1atan−1⁡xa+c=1a2∫drr2+ba2=1a21batan−1⁡rba+k=1abtan−1⁡atan⁡tb+k

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∫dta2sin2⁡t+b2cos2⁡t is equal to

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$\int \frac{d t}{a^{2} \sin^{2} t + b^{2} \cos^{2} t} is equal to$