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

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Correct option is D

∫1a2sin2⁡x+b2cos2⁡x=1abtan−1⁡atan⁡xb∴K=1ab=125

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∫dx4sin2⁡x+5cos2⁡x=Ktan−1⁡25tan⁡x+C, then K=

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