Show that \(\frac{\sin \left[ \left( n+1 \right)\theta -n\theta \right]}{\cos n\theta \cos \lef

Question

Show that $\frac{\sin \left[ \left( n+1 \right)\theta -n\theta \right]}{\cos n\theta \cos \left( n+1 \right)\theta }=\tan \left( n+1 \right)\theta -\tan \theta $.[2] Hence find, in terms of $n$ and $\theta $, and expression for[3] $\sec \theta \sec 2\theta +\sec 2\theta \sec 3\theta +\sec 3\theta \sec 4\theta +...+\sec n\theta \sec \left( n+1 \right)\theta $, where $n\in {{\mathbb{Z}}^{+}}$.

Accepted Answer

(ii) $\dfrac{\tan((n+1)\theta)-\tan\theta}{\sin\theta}$

2021 NJC P1 Q1

2021 NJC P1 Q1

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