Question

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

Answer 1

`\sin ((\pi)/(12))\cos ((7\pi)/(12))-\cos ((\pi)/(12))\sin ((7\pi)/(12))`

Let:

`\begin{gathered} A=(\pi)/(12) \\ B=(7\pi)/(12) \end{gathered}`

Using the sine difference identity:

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

Answer:

`\sin (-(\pi)/(2))`