Question

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

Trigonometric equation and identitie
ANSWERED
asked 2021-02-25
Solve the equation \(\frac{\sin^{2}\theta/}{cos \theta}= \sec \theta-\cos \theta\)

Answers (1)

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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