Question

Let 2cos 2x + 3cos x – 2 > 0 and x² + x – 2 < 0 (x is measured in radians), then number of integral values of x satisfying both the inequations is ______.

Options

• 0.00

• 1.00

• 2.00

• 3.00

Answer 1

Let 2cos 2x + 3cos x – 2 > 0 and x² + x – 2 < 0 (x is measured in radians), then number of integral values of x satisfying both the inequations is 2.00.

Explanation:

cos²x + 3cosx – 2 > 0 and x² + x – 2 < 0

⇒ (2cosx – 1)(cosx + 2) > 0

and (x – 1)(x + 2) < 0

⇒ `x∈(-π/3, π/3)` and x∈(–2, 1) or `x∈(-π/3, 1)`

 x = –1, 0