Question

To show that sin^2x+cos^2x=1 is equivalent to tan^2x+1=sec^2x,

what do you need divide sin^2x+cos^2x=1 by?

Answer 1

Let us divide both parts of the equality $\sin^2x+\cos^2x=1$ by $\cos^2 x$. Then we have $\frac{\sin^2x+\cos^2x}{\cos^2 x}=\frac{1}{\cos^2{x}}$ which is equivalent to $\frac{\sin^2x}{\cos^2 x}+\frac{\cos^2x}{\cos^2 x}=(\frac{1}{\cos{x}})^2$ and to $\tan^2x+1=\sec^2x.$