Prove the identity $$\(\frac{1+\sin \theta}{\cos \theta}+\frac{\cos \theta}{1+\sin \theta} \equiv \frac{2}{\cos \theta}\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s20_qp_11 Year：2020 Question No：7(a)
Answer:
\[
\frac{(1+\sin \theta)^{2}+\cos ^{2} \theta}{\cos \theta(1+\sin \theta)}
\]
Use of \(\sin ^{2} \theta+\cos ^{2} \theta=1 \rightarrow \frac{2+2 \sin \theta}{\cos \theta(1+\sin \theta)} \rightarrow \frac{2}{\cos \theta}\).
\frac{(1+\sin \theta)^{2}+\cos ^{2} \theta}{\cos \theta(1+\sin \theta)}
\]
Use of \(\sin ^{2} \theta+\cos ^{2} \theta=1 \rightarrow \frac{2+2 \sin \theta}{\cos \theta(1+\sin \theta)} \rightarrow \frac{2}{\cos \theta}\).
Knowledge points:
1.5.4 use the identities
Solution:
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