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$\int \frac{d x}{5 + 4 \cos x} = a \tan^{- 1} (b \tan \frac{x}{2}) + C, then$

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a=23,b=−13

a=23,b=13

a=−23,b=13

a=−23,b=−13

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Correct option is B

I=∫dx5+4cos⁡x=∫dx5sin2⁡x2+cos2⁡x2+4cos2⁡x2−sin2⁡x2=∫dx9cos2⁡x2+sin2⁡x2=∫sec2⁡x29+tan2⁡x2dx Now, I=∫2dt9+t2=23tan−1⁡t3+C∴ I=23tan−1⁡tan⁡x23+C Hence, a=23,b=13

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∫dx5+4cos⁡x=atan−1⁡btan⁡x2+C, then

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$\int \frac{d x}{5 + 4 \cos x} = a \tan^{- 1} (b \tan \frac{x}{2}) + C, then$