Q. 285.0( 1 Vote )

The number of dis

We have,

Applying C1 C1 + C2 + C3, we get

Taking (2cos X + sin X) common from the first column, we get

Applying R2 R2 – R1, we get

Applying R3 R3 – R1, we get

Expanding |A| along C1, we get

(2cos X + sin X) [(1){(sin X – cos X)(sin X – cos X)}]

(2cos X + sin X)(sin X – cos X)2 = 0

2cos X = -sin X or (sin X – cos X)2 = 0

tan X = -2 or tan X = 1

but tan X = -2 is not possible as for

So, tan X = 1

Hence, only one real distinct root exist.

Hence, the correct option is (c)

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