1.

The smallest positive value of `x`(in radians) satisfying the equation `(log)_(cosx)((sqrt(3))/2sinx)=2-(log)_(secx)(tanx)`is(a)`pi/(12)`(b) `pi/6`(c) `pi/4`(d) `pi/3`

Answer» `log_(cosx)(sqrt3/2sinx)=-log_(secx)(tanx)`
`log_(secx)(tanx)=(lntanx)/(lnsecx)=(lntanx)/(-lncosx)=-log_(cosx) tanx`
`log_cosxx(sqrt3/2sinx)=2+log_cosx(tanx)=log_cosx tanx`
`log_cosx(sqrt3/2cosx)=2`
`sqrt3/2cosx=cos^2x`
`cosx[cosx-sqrt3/2]=0`
`cosx=sqrt3/2`
`x=pi/6`.


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