Question

can someone please explain me how i can prove tan^2+1=sec^2x

Answer 1

Convert \(\tan(x)^2\) to \(({\sin(x)\over\cos(x)})^2\) and \(\sec(x)^2\) to \(({1\over\cos(x)})^2\)

Answer 2

tan^2(x)+1=sin^2(x)/cos^2(x) +1=(sin^2(x)+cos^2(x))/cos^2(x)....now you must know this sin^2(x)+cos^2(x)=1 so if you use that you get 1/cos^2(x)....that is the left side of your equality....now for the right side you must know that sec(x)=1/cos(x)...but you have sec^2(x)....so when you plug in (1/cos(x))^2 you get 1/cos^(x)....so left side=right side.....1/cos^2(x)=1/cos^2(x) so you proved it :D