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

The Expression Cos 90cos 30 Sin 90sin 30 Can Be Rewritten As Which Of The Following class=

Sagot :

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°.

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