CAIE P2 2006 November — Question 4

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2006
SessionNovember
TopicAddition & Double Angle Formulae
4
  1. Prove the identity $$\tan \left( x + 45 ^ { \circ } \right) - \tan \left( 45 ^ { \circ } - x \right) \equiv 2 \tan 2 x .$$
  2. Hence solve the equation $$\tan \left( x + 45 ^ { \circ } \right) - \tan \left( 45 ^ { \circ } - x \right) = 2 ,$$ for \(0 ^ { \circ } \leqslant x \leqslant 180 ^ { \circ }\).
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