Question

Solve frac{(sin theta+cos theta)}{cos theta}+frac{(sin theta-cos theta)}{cos theta}

Trigonometric equation and identitie
ANSWERED
asked 2021-03-04
Solve \(\frac{(\sin \theta+\cos \theta)}{\cos \theta}+\frac{(\sin \theta-\cos \theta)}{\cos \theta}\)

Answers (1)

2021-03-05
\(\frac{\sin(\theta)+\cos(\theta)}{\cos(\theta)}+\frac{\sin(\theta)-\cos(\theta)}{\cos(\theta)}=\)
Apply rule \(\frac{a}{c}\pm\frac{b}{c}=\frac{a\pm b}{c}\)
\(=(\sin(\theta)+\cos(\theta)+\sin(\theta)-\frac{\cos(\theta)}{\cos(\theta)}\)
\(=\frac{2\sin(\theta)}{\cos(\theta)}\)
Use the following identity: \(\sin(x)\cos(x)=\tan(x)\)
\(=2\tan(\theta)\)
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