Question

Write the expression as the sine, cosine, or tangent of an angle. cos 96° cos 15° + sin 96° sin 15°

Answer 1

cos(96° - 15°) or just cos(81°)

Answer 2

Answer:

$\cos 81^{\circ}$

Step-by-step explanation:

$\text{Consider the expression}\\\cos 96^{\circ}\cos 15^{\circ}+\sin 96^{\circ} \sin15^{\circ}\\\\\text{To write it as a single sine, cosine or tangent, we use the }\\\text{angle sum or difference formula.}\\\\\text{By the angle difference identity of cosine, we know that}\\\\\cos(A-B)=\cos A \cos B+\sin A \sin B$

$\text{The given expression is also of the form of the right side of above identity}\\\text{so we get}\\\\\cos 96^{\circ}\cos 15^{\circ}+\sin 96^{\circ} \sin15^{\circ}=\cos(96^{\circ}-15^{\circ})\\\\=\cos 81^{\circ}$