Show that $$\(\frac{\tan \theta}{1+\cos \theta}+\frac{\tan \theta}{1-\cos \theta} \equiv \frac{2}{\sin \theta \cos \theta}\)$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_s20_qp_13 Year：2020 Question No：7(a)
Answer:
\(\frac{\tan \theta}{1+\cos \theta}+\frac{\tan \theta}{1-\cos \theta}=\frac{\tan \theta(1-\cos \theta)+\tan \theta(1+\cos \theta)}{1-\cos ^{2} \theta}\)
\(=\frac{2 \tan \theta}{\sin ^{2} \theta}\)
\(=\frac{2 \sin \theta}{\cos \theta \sin ^{2} \theta}\)
\(=\frac{2}{\sin \theta \cos \theta} \mathbf{A G}\)
\(=\frac{2 \tan \theta}{\sin ^{2} \theta}\)
\(=\frac{2 \sin \theta}{\cos \theta \sin ^{2} \theta}\)
\(=\frac{2}{\sin \theta \cos \theta} \mathbf{A G}\)
Knowledge points:
1.5.4 use the identities
Solution:
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