Astudent was asked to prove cos(x+pi)=-cosx the students work follows, where was the students mistake?

The answer is the second ⇒ cosx cosπ - sinx sinπ

Step-by-step explanation:

∵ cos(x + π) = cosx cosπ - sinx sinπ

∵ cosπ = -1

∵ sinπ = 0

∴ cos(x + π) = cosx(-1) - sinx(0) = -cosx - 0 = -cosx

The mistake in the rule it will not give different answer because + 0 or - 0 give us the same answer but if the measure of angle not π the answer will change.

Note: cos(x + π) means the angle in the third quadrant and the value of cos in the third quadrant must be negative

The answer is: The mistake was in the second expression.

The second expression should be the follow:

The students are working with a cosine identity, cosine sum.

According to the theorem, cosine of a sum will be:

Where, for this case:

So, substituting we have:

So, the mistake was in the second step expression.

The expression should have been:

But why the result was correct even using a wrong expression?

The answer to that question is based on the value of sin(π) which is equal to 0.

Have a nice day!

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