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The smallest positive value of `x` (in radians) satisfying the equation `(log)_(cosx)((sqrt(3))/2sinx)=2-(log)_(secx)(tanx),` is `pi/(12)` (b) `pi/6`

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The smallest positive value of `x` (in radians) satisfying the equation `(log)_(cosx)((sqrt(3))/2sinx)=2-(log)_(secx)(tanx),` is `pi/(12)` (b) `pi/6` (c) `pi/4` (d) `pi/3`
A. `pi/12`
B. `pi/6`
C. `pi/4`
D. `pi/3`
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Correct Answer - B
We have `log_(cos x)(sqrt(3)/2 sin x)-log_(cos x) (tan x)=2`
`rArr log_(cos x)(sqrt(3)/2 cos x)=2`
`rArr sqrt(3)/2 cos x = cos^(2) x`
`rArr cos X(cos x - sqrt(3)/2)=0`
`:. X=pi/6 " "(x=pi/2" is rejected")`
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