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The smallest positive value of x (in radians) satisfying the equation $\log_{\cos x} (\frac{\sqrt{3}}{2} \sin x) = 2 - \log_{\sec x} (\tan x)$ , is

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Correct option is B

We have logcos⁡x⁡32sin⁡x−logcos⁡x⁡(tan⁡x)=2⇒logcos⁡x⁡32cos⁡x=2⇒32cos⁡x=cos2⁡x⇒cos⁡xcos⁡x−32=0∴x=π6x=π2 is rejected

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The smallest positive value of x (in radians) satisfying the equation logcos⁡x⁡32sin⁡x=2−logsec⁡x⁡(tan⁡x), is

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The smallest positive value of x (in radians) satisfying the equation $\log_{\cos x} (\frac{\sqrt{3}}{2} \sin x) = 2 - \log_{\sec x} (\tan x)$ , is