Hello!
The answer is: The mistake was in the second expression.
The second expression should be the follow:
[tex]cos(x+\pi)=cosxcos\pi-sinxsin\pi=-cosx[/tex]
Why?
The students are working with a cosine identity, cosine sum.
According to the theorem, cosine of a sum will be:
[tex]cos(a+b)=cosacosb-sinasinb[/tex]
Where, for this case:
[tex]a=x\\b=\pi[/tex]
So, substituting we have:
[tex]cos(x+\pi)=cosxcos\pi-sinxsin\pi=cosx*(-1)-sinx*(0)\\cos(x+\pi)=-cosx-0\\cos(x+\pi)=-cosx[/tex]
So, the mistake was in the second step expression.
The expression should have been:
[tex]cosxcos\pi-sinxsin\pi[/tex]
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!
