A-LevelMathematicsTrigonometry9709/33 · Oct/Nov 2025 · Q58 Marks
Show that cos4x+2sin²x-1 = 8sin⁴x-6 sin²x.
- (a)Show that cos4x+2sin²x-1 = 8sin⁴x-6 sin²x.[4]
- (b)Hence solve the equation cos4x+2sin²x−1 = 0 for -180° ≤ x ≤ 180°.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- Use correct double angle formula to express cos4x in terms of sin² 2x
- Use correct double angle formula to express cos 4x in terms of single angles
- Obtain a correct expression in sin x in any form
- Obtain the given answer 8 sin⁴ x – 6 sin²x
- Use correct double angle formula to express whole expression in terms of co s2x
- Use correct double angle formula to express 2 cos² 2x – 1 as cos 4x
- Use correct double angle formula to express whole expression as cos 4x – cos2x
- Obtain the given answer cos4x + 2sin2x – 1
- Obtain answers 0°, 180° and -180°
- Carry out a correct method to find a value of x in the given interval for 8 sin²x = 6
- Obtain answer, e.g. 60°
- Obtain remaining answers, e.g. -60°, 120° and -120° and no other in the interval
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