A-LevelMathematicsTrigonometry9709/32 · Feb/Mar 2018 · Q36 Marks
Using the expansions of cos(3x + x) and cos(3x – x), show that ½(cos 4x + cos 2x) = cos 3x cos x.
- (i)Using the expansions of cos(3x + x) and cos(3x – x), show that ½(cos 4x + cos 2x) = cos 3x cos x.[3]
- (ii)Hence show that ∫₀^(π/6) cos 3x cos x dx = √3/8.[3]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2018). The mark or mark type is shown in brackets.
- [B1] State correct expansion of cos(3x + x) or cos(3x – x)
- [M1] Substitute in ½(cos 4x + cos 2x)
- [A1] Obtain the given identity correctly AG
- [B1] Obtain integral ⅛sin 4x + ¼sin 2x
- [M1] Substitute limits correctly
- [A1] Obtain the given answer following full, correct and exact working AG
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