Prove that $1+\tan^2 x=\sec^2 x$

Question

I have no idea how to prove this. Does anyone know where to start? We're allowed to use other trigonometric identities but i'm not sure why these are useful.

Answer 1

Hint: start off with the identity $$\cos^2(x)+\sin^2(x) \equiv 1$$ and divide through by $\cos^2(x)$ and your result should follow immediately.

Answer 2

Hint : I hope you know that $\tan x=\dfrac{\sin x}{\cos x}$. Then use $\sin^2x+\cos^2 x=1$.

Answer 3

Start with the definitions in terms of $\sin$ and $\cos$. $$ \tan x = \frac{\sin x}{\cos x} \\ \sec x = \frac{1}{\cos x} $$