**Title: Expressing Trigonometric Functions as a Function of One Angle****Objective:**Learn how to express a trigonometric function involving two angles as a function of a single angle.**Problem:**Express the trigonometric expression as a function of one angle:\[ \cos 45^\circ \cos 22^\circ + \sin 45^\circ \sin 22^\circ \]**Solution Approach:**This expression can be simplified using the angle addition identity for cosine:\[ \cos(a + b) = \cos a \cos b - \sin a \sin b \]However, notice that our expression aligns with the form used in the sine angle addition identity:\[ \sin(a + b) = \sin a \cos b + \cos a \sin b \]Applying the identity, we can write:\[ \sin(45^\circ + 22^\circ) = \sin 45^\circ \cos 22^\circ + \cos 45^\circ \sin 22^\circ \]Thus, the expression simplifies to:\[ \sin(67^\circ) \]**Conclusion:**The expression \( \cos 45^\circ \cos 22^\circ + \sin 45^\circ \sin 22^\circ \) can be rewritten as \( \sin 67^\circ \).**Note:**There is faint text in the image suggesting further exploration of exact values and tangents, but it is not entirely visible for full transcription.

Name: **Title: Expressing Trigonometric Functions as a Function of One Angl
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
Description: **Title: Expressing Trigonometric Functions as a Function of One Angle****Objective:**Learn how to express a trigonometric function involving two angles as a function of a single angle.**Problem:**Express the trigonometric expression as a function o