Question

Which expression is equivalent to Sine (StartFraction pi Over 12 EndFraction) cosine (StartFraction 7 pi Over 12 EndFraction) minus cosine (StartFraction pi Over 12 EndFraction) sine (StartFraction 7 pi Over 12 EndFraction)?

Answer 1

Answer:

EndRoot Over 2 EndFraction

StartFraction pi Over 6 EndFraction, StartFraction StartRoot 3 EndRoot Over 2 EndFraction

Answer 2

On using the trigonometric identity sin(x-y) = sin(x)cos(y) - cos(x)sin(y), we calculate that  $sin(\frac{\pi }{12})cos(\frac{7\pi }{12}) - cos(\frac{\pi }{12} )sin(\frac{7\pi }{12} ) =sin(\frac{-\pi }{2} )$.

What are trigonometric identities?

Trigonometric identities are equations that relate to different trigonometric functions and are true for any value of the variable that is there in the domain.

$=sin(\frac{\pi }{12})cos(\frac{7\pi }{12}) - cos(\frac{\pi }{12} )sin(\frac{7\pi }{12} ) \\\\=sin(\frac{\pi }{12} -\frac{7\pi }{12})\\ \\ =sin(\frac{-\pi }{2} )$

Learn more about trigonometric identities here

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