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

`\cos 81^(\circ)`

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)`