Express in terms of one trig function

A question is this type if and only if it first asks to rewrite a trig expression (e.g. involving both sin and cos) in terms of a single trig function using an identity, and then solves the resulting equation.

1 questions · Moderate -0.3

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CAIE P1 2010 June Q5
7 marks Moderate -0.3
5 The function f is such that \(\mathrm { f } ( x ) = 2 \sin ^ { 2 } x - 3 \cos ^ { 2 } x\) for \(0 \leqslant x \leqslant \pi\).
  1. Express \(\mathrm { f } ( x )\) in the form \(a + b \cos ^ { 2 } x\), stating the values of \(a\) and \(b\).
  2. State the greatest and least values of \(\mathrm { f } ( x )\).
  3. Solve the equation \(\mathrm { f } ( x ) + 1 = 0\).