The number of distinct real roots of `|(sinx, cosx, cosx),(cos x,sin x,cos x),(cos x,cos x,sin x)|=0` in the interval `-(pi)/4 le x le (pi)/4` is

Options

A. 0
B. 2
C. 1
D. 3

Answer

C

Explanation

Using `C_(1) to C_(1)+C_(2)+C_(3)`
`Delta = |{:(sin x + 2 cos x,,cos x,,cos x),( sin x+ 2 cos x,,sin x,,cos x ),(sin x+2 cos x,,cos x ,, sin x):}|`
`= (sin x + 2 cos x) |{:(1,,cos x ,,cos x),(0,,sin x -cos x ,,0),(0,,0,,sin x - cos x):}|`
`=(sin x +2 cos x) (sin x-cos x)^(2)`
Thus , `Delta =0 rArr tan x =-2 " or " tan x=1`
As `-pi//4 le x le pi//r " we get " -1 le tan x le 1`
`:. tan x=1 rArr x= pi//4`