Question

The expression (cos 90°)(cos 30°) − (sin 90°)(sin 30°) can be rewritten as which of the following?

Answer 1

cos 120°

Explanation:

Given the trigonometric expression:

`\mleft(\cos 90\degree\mright)\mleft(\cos 30\degree\mright)-(\sin 90\degree)\mleft(\sin 30\degree\mright)`

By the trigonometric Law of Cosine Addition:

`\cos (A)\cos (B)-\sin (A)\sin (B)=\cos (A+B)`

Let A=90, and B=30. Therefore:

`\begin{gathered} (\cos 90\degree)(\cos 30\degree)-(\sin 90\degree)(\sin 30\degree)=\cos (90\degree+30\degree) \\ =\cos (120\degree) \end{gathered}`

The equivalent form of the expression is cos 120°.