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The number of distinct roots of |(sinx, ...

The number of distinct roots of `|(sinx, cosx, cosx),(cosx, sinx, cosx),(cosx,cosx,sinx)|=0` in the interval `-pi/4 le x le pi/4` is (A) 0 (B) 2 (C) 1 (4) 2

Text Solution

Verified by Experts

`|{(sinx-cosx,cosx-sinx,0),(0,sinx-cosx,cosx-sinx),(cosx,cosx,sinx):}|=0`
`(sinx-cosx)^2|{(1,-1,0),(0,1,-1),(cosx,cosx,sinx):}|=0` `sinx=cosx,x=pi/4`
`sinx=-cosx,x=-pi/4`
`cosx=0,x=pi/2`
option 2 is correct.
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