Edexcel C3 2007 January — Question 8

Exam BoardEdexcel
ModuleC3 (Core Mathematics 3)
Year2007
SessionJanuary
TopicReciprocal Trig & Identities

    1. Prove that
$$\sec ^ { 2 } x - \operatorname { cosec } ^ { 2 } x \equiv \tan ^ { 2 } x - \cot ^ { 2 } x$$ (ii) Given that $$y = \arccos x , \quad - 1 \leqslant x \leqslant 1 \text { and } 0 \leqslant y \leqslant \pi ,$$
  1. express arcsin \(x\) in terms of \(y\).
  2. Hence evaluate \(\arccos x + \arcsin x\). Give your answer in terms of \(\pi\).