Simplify sec(x+pi)

Question

 sec(x+pi)

Answer 1

It is good to recall the identity that

 

cos(x + π) = -cos(x)

 

Then

 

sec(x + π) = 1/cos(x + π) = 1/[-cos(x)] = -1/cos(x) = -sec(x)

Answer 2

sec(x+π) = 1 /cos(x+π)

 

              = 1 / [cosxcosπ - sinxsinπ]

 

              = 1 / (-cosx) = -secx