Question

Derive the remaining 2 Pythagorean identities from
Sin^2x+cos^2x=1

Answer 1

Let's start by finding the tangent square identity.
Divide each side by cos^2x,\[\Large\rm \frac{\sin^2x}{\cos^2x}+1=\frac{1}{\cos^2x}\]

Answer 2

It can be simplified a bit from there,
Remember your identities?\[\Large\rm \frac{\sin x}{\cos x}=\tan x,\qquad\qquad\qquad \frac{1}{\cos x}=\sec x\]