Question

Verify that tan^2(x)+6=sec^2(x)+5

Answer 1

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