Answer:
cos 120°
Explanation:
Given the trigonometric expression:
[tex]\mleft(\cos 90\degree\mright)\mleft(\cos 30\degree\mright)-(\sin 90\degree)\mleft(\sin 30\degree\mright)[/tex]
By the trigonometric Law of Cosine Addition:
[tex]\cos (A)\cos (B)-\sin (A)\sin (B)=\cos (A+B)[/tex]
Let A=90, and B=30. Therefore:
[tex]\begin{gathered} (\cos 90\degree)(\cos 30\degree)-(\sin 90\degree)(\sin 30\degree)=\cos (90\degree+30\degree) \\ =\cos (120\degree) \end{gathered}[/tex]
The equivalent form of the expression is cos 120°.
