Question

The number of distinct real roots of the equation |(cosx, sinx, sinx), (sinx, cosx, sinx), (sinx, sinx, cosx)| = 0  in the interval [-π/4, π/4] is

(A) 1

(B) 4

(C) 2

(D) 3

Answer 1

Answer is (C) 2

⇒ (cosx  - + sinx)²(cosx + 2sinx) = 0

Therefore, 2sinx + cosx = 0 or sinx = cosx

For 2sinx + cosx = 0, tan x = − 1/2 ; therefore, one solution in

x ∈ [-π/4, π/4]

For sinx = cosx, one solution in x ∈ [- π/4, π/4],

Therefore, the total number of solutions is 2.