Is this answer a mistake?

ma005

#1

MA005 section 3.5 Practice Problems number 37.
The question is: Find the derivative of: d/dz sqrt(1+(cosz)^2)
The answer given is: (-sin(2z))/(2 sqrt(1+(cosz)^2)
Shouldn’t the answer be: -coszsinz/(sqrt(1+(cosz)^2)?
If no, then why not?
link to the question page: https://s3.amazonaws.com/saylordotorg-resources/wwwresources/site/wp-content/uploads/2012/12/MA005-3.5-Chain-Rule.pdf
link to the answer page: https://resources.saylor.org/wwwresources/archived/site/wp-content/uploads/2012/07/MA005_Unit-3.11_Odd-Solutions.pdf


#2

I think your answer is correct, but so is the given answer. There was a bit more simplification in the given answer where the trig double angle formula was used. In your case, -cos(z)sin(z)=sin(2*z)/2.

Math answers often appear in different but equivalent forms .

Good Luck!