The equation k cos ⁡ x - 3 sin ⁡ x = k + 1 is solvable only if

Step-by-step solution

k cos ⁡ x - 3 sin ⁡ x = k + 1 For a solution k + 1 ≤ k 2 + - 3 2 ⇒ k + 1 ≤ k 2 + 9 On squaring both sides, we get, k 2 + 1 + 2 k ≤ k 2 + 9 ⇒ 2 k ≤ 8 ⇒ k ≤ 4 ⇒ k ∈ - ∞ , 4