Given the function value, find a cofunction of another angle with the same value. Express your answer in simplest form using radians. \[ \cos \frac{\pi}{12}=\frac{\sqrt{6}+\sqrt{2}}{4}= \]

Step 1 ：Given the function value, find a cofunction of another angle with the same value. Express your answer in simplest form using radians.

Step 2 ：The cosine function is a cofunction of the sine function. This means that the cosine of an angle is equal to the sine of its complement. In terms of radians, the complement of an angle is \(\frac{\pi}{2}\) - the angle.

Step 3 ：So, to find a cofunction of another angle with the same value as \(\cos \frac{\pi}{12}\), we need to find \(\sin(\frac{\pi}{2} - \frac{\pi}{12})\).

Step 4 ：Calculate the complement of the angle \(\frac{\pi}{12}\): \(\frac{\pi}{2} - \frac{\pi}{12} = \frac{5\pi}{12}\).

Step 5 ：\(\boxed{\sin \frac{5\pi}{12}}\) is the cofunction of another angle with the same value as \(\cos \frac{\pi}{12}\).