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Note: Enter your answer and show all the steps that you use to solve this problem in the spaceprovided.Show that sin (x +pi ) = - sin xShow all of your work

Note Enter Your Answer And Show All The Steps That You Use To Solve This Problem In The SpaceprovidedShow That Sin X Pi Sin XShow All Of Your Work class=

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ANSWER and EXPLANATION

We want to prove that:

[tex]\sin(x+\pi)=-\sin x[/tex]

Let us start with the left-hand side of the equation.

Using trigonometric identities for sine, we have that:

[tex]\sin(A+B)=\sin A\cos B+\sin B\cos A[/tex]

Applying this identity to the left-hand side of the equation:

[tex]\sin(x+\pi)=\sin x\cos\pi+\sin\pi\cos x[/tex]

We know that:

[tex]\begin{gathered} \cos\pi=-1 \\ \sin\pi=0 \end{gathered}[/tex]

Substituting those values into the above expression:

[tex]\begin{gathered} \sin x(-1)+(0)\cos x \\ \Rightarrow-\sin x \end{gathered}[/tex]

Since the left-hand side of the equation is equal to the right-hand side, we have that it has been proven.

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