The first and second terms of an arithmetic progression are $$\(\frac{1}{\cos ^{2} \theta}\)$$ and $$\(-\frac{\tan ^{2} \theta}{\cos ^{2} \theta}\)$$, respectively, where $$\(0<\theta<\frac{1}{2} \pi\)$$. Show that the common difference is $$\(-\frac{1}{\cos ^{4} \theta}\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_w20_qp_13 Year：2020 Question No：7(a)
Answer:
\((d=)-\frac{\tan ^{2} \theta}{\cos ^{2} \theta}-\frac{1}{\cos ^{2} \theta}\)
\(-\frac{\sin ^{2} \theta}{\cos ^{4} \theta}-\frac{1}{\cos ^{2} \theta}\) or \(\frac{-\sec ^{2} \theta}{\cos ^{2} \theta}\)
\(\frac{-\sin ^{2} \theta-\cos ^{2} \theta}{\cos ^{4} \theta}\) or \(\frac{-\frac{1}{\cos ^{2} \theta}}{\cos ^{2} \theta}\)
\(-\frac{1}{\cos ^{4} \theta}\)
\(-\frac{\sin ^{2} \theta}{\cos ^{4} \theta}-\frac{1}{\cos ^{2} \theta}\) or \(\frac{-\sec ^{2} \theta}{\cos ^{2} \theta}\)
\(\frac{-\sin ^{2} \theta-\cos ^{2} \theta}{\cos ^{4} \theta}\) or \(\frac{-\frac{1}{\cos ^{2} \theta}}{\cos ^{2} \theta}\)
\(-\frac{1}{\cos ^{4} \theta}\)
Knowledge points:
1.5.4 use the identities
1.6.2 recognise arithmetic and geometric progressions
Solution:
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