Question

The equation sin⁴x - 2cos²x + a² = 0 The equation if

(A)  -√3 ≤ a ≤ √3

(B)  -√2 ≤ a ≤ √2

(C)  −1 ≤ a ≤ 1

(D)  None of these

Answer 1

Correct option (B)  -√2 ≤ a ≤ √2 

We have sin⁴ x - 2cos² x + a² = 0. Let y = sin² x. Then

For y to be real, Discriminant ≥ 0.

So  4 - 4(a² - 2)≥0 ⇒ a² ≤ 3   .....(1)

But  sin² x = y. Therefore 0 ≤1 ≤ y . So

From Eqs. (1) and (2), a² ≤ 2