If ∫cosxcos2xdx=A ln1+2sinx1−2sinx+c , then A =

∫cosxcos2xdx=∫cosx1−2sin2xdx 122ln1+2sinx1−2sinx+c∴ A =122

If ∫cosxcos2xdx=A ln1+2sinx1−2sinx+c , then A =

∫cosxcos2xdx=∫cosx1−2sin2xdx 122ln1+2sinx1−2sinx+c∴ A =122

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If $\int \frac{\cos x}{\cos 2 x} d x = A$ $\ln |\frac{1 + \sqrt{2} \sin x}{1 - \sqrt{2} \sin x}| + c$ , then A =

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_{$\frac{1}{2 \sqrt{2}}$}

_{$\frac{1}{2}$}

_{$\frac{1}{\sqrt{2}}$}

_$\sqrt{2}$

answer is A.

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Detailed Solution

$\int \frac{\cos x}{\cos 2 x} d x = \int \frac{\cos x}{1 - 2 \sin^{2} x} d x$

$\frac{1}{2 \sqrt{2}} \ln |\frac{1 + \sqrt{2} \sin x}{1 - \sqrt{2} \sin x}| + c$

$∴ A = \frac{1}{2 \sqrt{2}}$

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If ∫cosxcos2xdx=A ln1+2sinx1−2sinx+c , then A =

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If $\int \frac{\cos x}{\cos 2 x} d x = A$ $\ln |\frac{1 + \sqrt{2} \sin x}{1 - \sqrt{2} \sin x}| + c$ , then A =