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$If y - \cos x \cdot \frac{d y}{d x} = y^{2} (1 - \sin x) \cos x, y (0) = 1 then y (\frac{π}{3})$

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Correct option is B

Dividing the given DE by y2cos⁡x−1y2⋅dydx+sec⁡x⋅1y=1−sin⁡x⇒ddx1y+sec⁡x⋅1y=1−sin⁡xI.F=∫e sec⁡x⋅dx=sec⁡x+tan⁡x Solution if 1y(sec⁡x+tan⁡x)=∫(1−sin⁡x)(1+sin⁡x)cos⁡x=sin⁡x+cx=0,y=1,⇒c=1∴y=sec⁡x,⇒yπ3=2

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