Write each function as an expression involving functions of θ or x alone. See Example 2.
cos(45° - θ)

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Recall the cosine difference identity: \(\cos(A - B) = \cos A \cos B + \sin A \sin B\).

Identify the angles in the expression: here, \(A = 45^\circ\) and \(B = \theta\).

Apply the identity to rewrite \(\cos(45^\circ - \theta)\) as \(\cos 45^\circ \cos \theta + \sin 45^\circ \sin \theta\).

Substitute the known exact values for \(\cos 45^\circ\) and \(\sin 45^\circ\), which are both \(\frac{\sqrt{2}}{2}\).

Write the final expression as \(\frac{\sqrt{2}}{2} \cos \theta + \frac{\sqrt{2}}{2} \sin \theta\), involving only functions of \(\theta\).

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