# Solve the equation frac{sin^{2}theta/}{cos theta}= sec theta-cos theta

Question
Solve the equation $$\frac{\sin^{2}\theta/}{cos \theta}= \sec \theta-\cos \theta$$

2021-02-26
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: $$\sec \theta=\frac{1}{\cos \theta}$$
$$\frac{\sin^{2}\theta}{\cos \theta}= \sec \theta-\cos \theta$$

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