If ∫$$cos4$$⁡$$xsin2$$⁡$$xdx=Acot$$⁡$$x+Bsin$$⁡$$2x+C2x+D$$, then

Correct option is 2B=−14,C=−3

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If $\int \frac{\cos^{4} x}{\sin^{2} x} dx = Acot x + Bsin 2 x + \frac{C}{2} x + D$ , then

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A=−2,B=14

B=−14,C=−3

B=14,C=−3

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detailed solution

Correct option is B

We have, 1=∫cos4⁡xsin2⁡xdx=∫1−sin2⁡x2sin2⁡xdx=∫cosec2⁡x+sin2⁡x−2dx=−cot⁡x+12x−sin⁡2x2−2x+D=−cot⁡x−14sin⁡2x−32x+D∴A=−1,B=−14,C=−3

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If ∫cos4⁡xsin2⁡xdx=Acot⁡x+Bsin⁡2x+C2x+D, then

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If $\int \frac{\cos^{4} x}{\sin^{2} x} dx = Acot x + Bsin 2 x + \frac{C}{2} x + D$ , then