The number of integral values of $k$ for which the equation $7 \cos x+5 \sin x=2 k+1$ has a solution

Question

The number of integral values of $k$ for which the equation $7 \cos x+5 \sin x=2 k+1$ has a solution in

Professor PC Thomas Classes · Answer

Condition for solution: $-\sqrt{74} \le 2k+1 \le \sqrt{74}$.