129k views
5 votes
Review the proof of the identity cos(-A) = -COSA. at which step was an error made

Review the proof of the identity cos(-A) = -COSA. at which step was an error made-example-1
User Adie
by
6.9k points

2 Answers

4 votes

Answer: A. Step 1

Step-by-step explanation: on edge

User Tim Yao
by
6.4k points
6 votes

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.

Therefore, step 1 is the mistake in the given demonstration.

User Waldrumpus
by
7.3k points