Question

The equations Kcosx - 3sin x = K + 1 is solvable only if K belongs to the interval

• A. [1, +∞)
• B. [-4, 4]
• C. (-∞, 4]
• D. (-∞, ∞)

Answer 1

The correct option is C

(-∞, 4]

The conditions is | $\frac{K+1}{\sqrt{K^2+9}}$| ≤ 1

⇒ $(K+1{)}^2$ ≤ $K^2$ + 9

⇒ K ≤ 4