DeterminantHard
Question
The number of distinct real roots of 
= 0 in the interval - 
≤ x ≤ is
= 0 in the interval - ≤ x ≤ is Options
A.0
B.2
C.1
D.3
Solution
Given, 
= 0
Applying C1 → C1 + C2 + C3
= (cos x + sin x)
Applying R2 → R2 - R1, R3 → R3 - R1
⇒ (2 cos x + sin x)
⇒ (2cos x + sin x)(sin x - cos x)2 = 0
⇒ 2 cos x + sin x = 0 or sin x - cos x = 0
⇒ 2 cos x = - sin x or sin x = cos x
⇒ cot x = - 1/2 gives no solution in -
≤ x ≤
and sin x = cos x ⇒ tan x = 1
⇒ x = π / 4
= 0Applying C1 → C1 + C2 + C3
= (cos x + sin x)
Applying R2 → R2 - R1, R3 → R3 - R1
⇒ (2 cos x + sin x)
⇒ (2cos x + sin x)(sin x - cos x)2 = 0
⇒ 2 cos x + sin x = 0 or sin x - cos x = 0
⇒ 2 cos x = - sin x or sin x = cos x
⇒ cot x = - 1/2 gives no solution in -
≤ x ≤ and sin x = cos x ⇒ tan x = 1
⇒ x = π / 4
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