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$The solution of \sec^{2} θ d θ + \tan θ (1 - r \tan θ) d r = 0 is$

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tanθ=r−1+cer

tanθ=r+ce−r

cotθ=r−1+cer

cotθ=r+ce−r

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detailed solution

Correct option is C

dθdr+tan⁡θsec2⁡θ=rtan2⁡θsec2⁡θcos⁡ec2θdθdr+cot⁡θ=r Put cot⁡θ=u⇒−cosec2⁡θdθ=du⇒dudr−u=−r I.F =e−r G.S. is ue−r=−r∫e−rdr⇒cot⁡θ=r−1+cer

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The solution of sec2⁡θdθ+tan⁡θ(1−rtan⁡θ)dr=0 is

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$The solution of \sec^{2} θ d θ + \tan θ (1 - r \tan θ) d r = 0 is$