In right triangle \( D A N, \mathrm{~m} \angle A=90^{\circ} \). Which statement must always true? \( \begin{array}{ll}\text { (1) } \cos D=\cos N & \text { (3) } \sin A=\cos N \\ \text { (2) } \cos D=\sin N & \text { (4) } \cos A=\tan N\end{array} \)

Let's analyze the given right triangle \( DAN \) with \( \angle A = 90^\circ \). The other two angles, \( \angle D \) and \( \angle N \), are complementary, meaning \( \angle D + \angle N = 90^\circ \). We need to evaluate each statement to determine which is always true: 1. **\( \cos D = \cos N \)** - Since \( \angle D \) and \( \angle N \) are complementary, \( \cos D = \sin N \), not \( \cos N \). - **This statement is false.** 2. **\( \cos D = \sin N \)** - As mentioned, \( \cos D = \sin N \) because \( \angle D \) and \( \angle N \) are complementary. - **This statement is always true.** 3. **\( \sin A = \cos N \)** - \( \sin A = \sin 90^\circ = 1 \). - \( \cos N \) is not necessarily 1 unless \( N = 0^\circ \), which is not possible in a triangle. - **This statement is false.** 4. **\( \cos A = \tan N \)** - \( \cos A = \cos 90^\circ = 0 \). - \( \tan N \) is not zero unless \( N = 0^\circ \), which is not possible in a triangle. - **This statement is false.** **Conclusion:** Only statement **(2) \( \cos D = \sin N \)** must always be true. **Answer:** (2) \(\cos D = \sin N\) is always true.