Review the proof of the identity cos(-A) = -COSA. at which step was an error made

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asked Oct 22, 2023 129k views

2 Answers

Waldrumpus · Answer 1 · 2023-10-29T11:57:50+0000

The given identity is

$\cos (\pi-A)=-\cos A$

Step 1 is about the trigonometric identify of angle difference which states

$\cos (\pi-A)=\cos \pi\cdot\cos A+\sin \pi\cdot\sin A$

So, the first step is wrong since they used subtraction instead of addition.

Step 2 is about solving each trigonometric function of pi. We know that the cosine of pi is -1, and the sine of pi is 0. So, we have

$(-1)\cdot\cos A+0\cdot\sin A$

The second step is correct.

Steps 3 and 4 are about solving the products.

$(-1)\cdot\cos A+0\cdot\sin A=-\cos A+0$

Steps 3 and 4 are correct.

Step 5 is also correct since the zero doesn't change the cosine function.