Question

sin x + cos = y² - y + a has no value of x for any y if ‘a’ belongs to

(A)  (0,√3)

(B)  (-√3,0)

(C)  (-∞, -√3)

(D)  (√3,∞)

Answer 1

Correct option (D)  (√3,∞)

Given equation is

sin x + cos x = y² - y + a

we know that -√2≤ sin x + cos x ≤ √2

Now, the given equation with root be satisfied for any y² - y + a ≥ √2 or y²  - y + a ≤ - √2 for all y, which is not possible Therefore,