(sin 30+ cos 30°) (sin 60° - cos 60°)

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05-07-2024
Mathematics

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(sin 30+ cos 30°) (sin 60° - cos 60°)

Sagot :

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Bqreidn Bqreidn · Answer 1 · 2024-07-05T09:03:08-04:00

Answer:

0.5

Step-by-step explanation:

[tex](\sin30+\cos30)(\sin60-\cos60)\texttt{ // Expand}\\=\sin30\sin60-\sin30\cos60+\sin60\cos30-\cos30\cos60\texttt{ // Group}\\=-(\cos30\cos60-\sin30\sin60)+(\sin60\cos30-\cos60\sin30)\\\\\texttt{Recall:}\\\to \cos\alpha\cos\beta - \sin\alpha\sin\beta=\cos(\alpha + \beta)\\\to\sin\alpha\cos\beta-\cos\alpha\sin\beta=\sin(\alpha - \beta)\\\\=-\cos(30 + 60)+\sin(60 - 30)\\=-\cos(90)+\sin(30)\\=-0+\frac12\\=\frac12[/tex]

The value of (sin30° + cos30°)(sin60° - cos60°) is 0.5.

Sagot :

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