Show constant value or identity

A question is this type if and only if it requires proving that an expression has a constant value for all θ, or showing an algebraic identity involving harmonic expressions.

1 questions · Standard +0.3

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CAIE P1 2013 June Q5
7 marks Standard +0.3
5 It is given that \(a = \sin \theta - 3 \cos \theta\) and \(b = 3 \sin \theta + \cos \theta\), where \(0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }\).
  1. Show that \(a ^ { 2 } + b ^ { 2 }\) has a constant value for all values of \(\theta\).
  2. Find the values of \(\theta\) for which \(2 a = b\).