When the maximum value of the function $f ( x ) = 2 \cos ^ { 2 } x + k \sin 2 x - 1$ is $\sqrt { 10 }$, what is the value of the positive constant $k$? [3 points] (1) 1 (2) 2 (3) 3 (4) 4 (5) 5
When the maximum value of the function $f ( x ) = 2 \cos ^ { 2 } x + k \sin 2 x - 1$ is $\sqrt { 10 }$, what is the value of the positive constant $k$? [3 points]\\
(1) 1\\
(2) 2\\
(3) 3\\
(4) 4\\
(5) 5