Work with the left side. Use the Pythagorean identity:

\(\sin^{2}\theta+\cos^{2}\theta=1\)

\(\frac{\sin^{2}\theta}{cos \theta}=\frac{1-\cos^{2}\theta}{cos \theta}\)

Separate as:

\(\frac{\sin^{2}\theta}{cos \theta}=1/\cos \theta-\frac{\cos^{2}\theta}{cos \theta}\)

\(\frac{\sin^{2}\theta}{\cos \theta}=\frac{1}{\cos \theta}-\cos \theta\)

Use the reciptiocal identity: \(\sec \theta=\frac{1}{\cos \theta}\)

\(\frac{\sin^{2}\theta}{\cos \theta}= \sec \theta-\cos \theta\)

\(\sin^{2}\theta+\cos^{2}\theta=1\)

\(\frac{\sin^{2}\theta}{cos \theta}=\frac{1-\cos^{2}\theta}{cos \theta}\)

Separate as:

\(\frac{\sin^{2}\theta}{cos \theta}=1/\cos \theta-\frac{\cos^{2}\theta}{cos \theta}\)

\(\frac{\sin^{2}\theta}{\cos \theta}=\frac{1}{\cos \theta}-\cos \theta\)

Use the reciptiocal identity: \(\sec \theta=\frac{1}{\cos \theta}\)

\(\frac{\sin^{2}\theta}{\cos \theta}= \sec \theta-\cos \theta\)