A-LevelMathematicsTrigonometry9709/12 · Oct/Nov 2009 · Q56 Marks
Prove the identity (sin x + cos x)(1 − sin x cos x) = sin³ x + cos³ x.
- (i)Prove the identity (sin x + cos x)(1 − sin x cos x) = sin³ x + cos³ x.[3]
- (ii)Solve the equation (sin x + cos x)(1 − sin x cos x) = 9 sin³ x for 0° ≤ x ≤ 360°.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2009). The mark or mark type is shown in brackets.
- [1] Needs 4 terms from the product.
- [1] Needs to be used once. (sin²x = 1 - cos²x or cos²x = 1 - sin²x)
- [1] All ok.
- [1] Uses part (i) -> 8 sin³x = cos³x (M1)
- [1] Uses tan x = sin x ÷ cos x -> tan³x = k (M1)
- [1] x = 26.6° and 206.6° (Co. √ for 180° + first answer and providing there are no other answers in range. A1 B1√)
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →