Posted by Anonymus on Monday, February 28, 2011 at 5:04pm.
Rewrite equation:
tan^2(x)+6=sec^2(x)+5
6-5=sec^2(x)tan^2(x)
sec^2(x)-tan^2(x)=1
Now you must verify that:
sec^2(x)-tan^2(x)=1
tan(x)=sin(x)/cos(x)
tan(x)=sin(x)*sec(x)
tan^2(x)=sin^2(x)*sec^2(x)
sec^2(x)-tan^2(x)=
sec^2(x)-sin^2(x)*sec^2(x)=
sec^2(x)*[1-sin^2(x)]
sin^2(x)+cos^2(x)=1
cos^2(x)=1-sin^2(x)
sec^2(x)*[1-sin^2(x)]=
sec^2(x)*cos^2(x)
sec(x)=1/cos(x)
sec^2(x)=1/cos^2(x)
sec^2(x)*cos^2(x)=
[1/cos^2(x)]*cos^2(x)=1