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The smallest positive `x` satisfying the equation `(log)_(cosx)sinx+(log)_(sinx)cosx=2` is `pi/2` (b) `pi/3` (c) `pi/4` (d) `pi/6`

A

`pi//2`

B

`pi//3`

C

`pi//4`

D

`pi//6`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `log_(cos x) sin x=t`, then the given equation is `t+1/t=2`
or `(t-1)^(2)=0`
or `t=1`
or `log_(cos x) sin x=1 or sin x = cos x`
`rArr tan x=1`
or `x=pi//4`
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