How do you show $\sin(180^\circ - 2x) = \sin(2x)$

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My approach would be let $2x$ become $q$ and $\sin(180-q)=\sin(q)$ therefore $\sin(q)=\sin(2x)$ but I think there is a better proof.

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1 Answer

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Hint: Use the subtraction formula $$\sin (a-b) = \sin a \cos b - \cos a \sin b$$ with $a = 180^{\circ}$ and $b = 2x$. Also note where $180^{\circ}$ lies and how it will affect one of the trigonometric values.

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