CAIE P1 2019 June — Question 4

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2019
SessionJune
TopicTrig Proofs

4 Angle \(x\) is such that \(\sin x = a + b\) and \(\cos x = a - b\), where \(a\) and \(b\) are constants.
  1. Show that \(a ^ { 2 } + b ^ { 2 }\) has a constant value for all values of \(x\).
  2. In the case where \(\tan x = 2\), express \(a\) in terms of \(b\).