| Exam Board | Edexcel |
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| Module | C3 (Core Mathematics 3) |
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| Topic | Trig Proofs |
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4. (i) Prove, by counter-example, that the statement
$$\text { " } \sec ( A + B ) \equiv \sec A + \sec B , \text { for all } A \text { and } B \text { " }$$
is false.
(ii) Prove that
$$\tan \theta + \cot \theta \equiv 2 \operatorname { cosec } 2 \theta , \quad \theta \neq \frac { n \pi } { 2 } , n \in \mathbb { Z }$$