Question

how do I prove that sec(pi-x)=-sec(x)?

Answer 1

Change the left-side of the equation first in terms of cosine:\[\bf \sec(\pi-x)=\frac{ 1 }{ \cos(\pi-x) }\]Now use the sum/difference formula for cos(a - b) to change the denominator:\[\bf =\frac{ 1 }{ \cos(\pi)\cos(x)+\sin(\pi)\sin(x) }=\frac{ 1 }{ (-1)\cos(x)+(0)\sin(x) }=-\frac{ 1 }{ \cos(x) }\]\[\bf = -\sec(x)\]That's it.

Answer 2

wow... thank you so much! i got the first two two steps down, but was stumped. I had 60 problems to do in my college trig homework and am down to the four hardest ones. I really appreciate this Genius12!

Answer 3

yw.