A-LevelMathematicsTrigonometry9709/31 · Oct/Nov 2022 · Q67 Marks
Prove the identity cos 4θ + 4 cos 2θ + 3 = 8 cos⁴ θ.
- (a)Prove the identity cos 4θ + 4 cos 2θ + 3 = 8 cos⁴ θ.[4]
- (b)Hence solve the equation cos 4θ + 4 cos 2θ = 4 for 0° ≤ θ ≤ 180°.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [B1] (a) Express cos 4θ in terms of cos 2θ and/or sin 2θ
- [B1] (a) Express cos 2θ in terms of cos θ and/or sin θ
- [B1] (a) Expand to obtain a correct expression in terms of cos θ
- [B1] (a) Reduce correctly to cos 4θ + 4 cos 2θ + 3 = 8 cos⁴ θ (AG)
- [M1] (b) Use the identity and carry out method to calculate a root
- [A1] (b) Obtain answer, e.g. 14.7°
- [A1] (b) Obtain second answer, e.g. 165.3°, and no other in the given interval
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