Aubrey tried to prove that $$\sin (\theta)=\cos (180^{\circ}-\theta)$$. ![](http://admin.getprephub.com/media/editor/ra20_20230123190907837407.png) What is the first mistake in Aubrey's proof?

Answer $$<A+<B+<C=180^{\circ}$$ But,$$<A=90^{\circ}$$ Therefore, $$90^{\circ}+<B+<C=180^{\circ}$$ Or, $$<B+<C=180^{\circ}-90^{\circ}=90^{\circ}$$ Or, $$<B=90^{\circ}-<C$$ Therefore $$<B$$ and $$<C$$ are complementary to each other, not supplementary.

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Aubrey tried to prove that $\sin (\theta)=\cos (180^{\circ}-\theta)$ .

What is the first mistake in Aubrey’s proof?

Select all that apply :

$\angle B$ and $\angle C$ are complementary, not supplementary.

Aubrey used the wrong sides in her ratio for $\sin (\theta)$ .

Aubrey used the wrong sides in her ratio for $\cos (180^{\circ}-\theta)$ .

Aubrey substituted a value that wasn’t equivalent to the one she replaced.

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