Solve using quadratic in trig function

A question is this type if and only if the equation can be rewritten as a quadratic in sin x, cos x, or similar, requiring substitution and the quadratic formula or factoring.

2 questions · Standard +0.3

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CAIE P1 2022 June Q11
10 marks Standard +0.3
11 The function f is given by \(\mathrm { f } ( x ) = 4 \cos ^ { 4 } x + \cos ^ { 2 } x - k\) for \(0 \leqslant x \leqslant 2 \pi\), where \(k\) is a constant.
  1. Given that \(k = 3\), find the exact solutions of the equation \(\mathrm { f } ( x ) = 0\).
  2. Use the quadratic formula to show that, when \(k > 5\), the equation \(\mathrm { f } ( x ) = 0\) has no solutions.
    If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.
OCR C2 Q4
8 marks Standard +0.3
4. Find all values of \(x\) in the interval \(0 \leq x < 360 ^ { \circ }\) for which $$2 \sin ^ { 2 } x - 2 \cos x - \cos ^ { 2 } x = 1$$ giving non-exact answers to 1 decimal place.