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STEP Support Programme

Assignment 16

In question 2ii the hints and partial solutions say you should end up with 0=2s^3-2s^2-s+1 however I don't understand why it's +1 since 2cos2A=2(1-2sin^2A)=2-4sin^2A and so I'm confused about why it's +1 rather than +2. Thanks for the help.

We have:
sin3AsinA=2cos2A3sinA4sin3AsinA=2(12sin2A)2sinA4sin3A=24sin2AsinA2sin3A=12sin2A

Basically, it is "+1" as you can divide throughout by 2.

Useful Links

Underground Mathematics: Selected worked STEP questions

STEP Question database

University of Cambridge Mathematics Faculty: What do we look for?

University of Cambridge Mathematics Faculty: Information about STEP

University of Cambridge Admissions Office: Undergraduate course information for Mathematics

Stephen Siklos' "Advanced Problems in Mathematics" book (external link)

MEI: Worked solutions to STEP questions (external link)

OCR: Exam board information about STEP (external link)