Simplify ((sec(x)+1)(sec(x)-1))/(sin(x)^2)

$\frac{(\sec (x) + 1) (\sec (x) - 1)}{\sin^{2} (x)}$

Simplify the numerator.

Rewrite $\sec (x)$ in terms of sines and cosines.

$\frac{(\frac{1}{\cos (x)} + 1) (\sec (x) - 1)}{\sin^{2} (x)}$

Rewrite $\sec (x)$ in terms of sines and cosines.

$\frac{(\frac{1}{\cos (x)} + 1) (\frac{1}{\cos (x)} - 1)}{\sin^{2} (x)}$

Simplify the numerator.

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

$\frac{(\sec (x) + 1) (\frac{1}{\cos (x)} - 1)}{\sin^{2} (x)}$

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

$\frac{(\sec (x) + 1) (\sec (x) - 1)}{\sin^{2} (x)}$