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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π12

π6

π4

π3

answer is B.

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Detailed Solution

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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