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Which expression is equivalent to sin(71(1) cos (72) - cos () sin (77.)?1?O cos (5)O sin (5)COS2012sin

Which Expression Is Equivalent To Sin711 Cos 72 Cos Sin 771O Cos 5O Sin 5COS2012sin class=

Sagot :

[tex]\sin (\frac{\pi}{12})\cos (\frac{7\pi}{12})-\cos (\frac{\pi}{12})\sin (\frac{7\pi}{12})[/tex]

Let:

[tex]\begin{gathered} A=\frac{\pi}{12} \\ B=\frac{7\pi}{12} \end{gathered}[/tex]

Using the sine difference identity:

[tex]\begin{gathered} \sin (A)\cos (B)-\cos (A)\sin (B)=\sin (A-B) \\ so\colon \\ \sin (\frac{\pi}{12})\cos (\frac{7\pi}{12})-\cos (\frac{\pi}{12})\sin (\frac{7\pi}{12})=\sin (\frac{\pi}{12}-\frac{7\pi}{12}) \\ \sin (\frac{\pi}{12}-\frac{7\pi}{12})=\sin (-\frac{6\pi}{12}) \\ \sin (-\frac{\pi}{2}) \end{gathered}[/tex]

Answer:

[tex]\sin (-\frac{\pi}{2})[/tex]

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