A-LevelMathematicsTrigonometry9709/31 · Oct/Nov 2017 · Q47 Marks
Prove the identity tan(45° + x) + tan(45° – x) = 2 sec 2x.
- (i)Prove the identity tan(45° + x) + tan(45° – x) = 2 sec 2x.[4]
- (ii)Hence sketch the graph of y = tan(45° + x) + tan(45° − x) for 0° ≤ x ≤ 90°.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [M1] (i) Use correct tan(A+B) formula and express the LHS in terms of tan x
- [A1] (i) Using tan 45Y=1 express LHS as a single fraction
- [M1] (i) Use Pythagoras or correct double angle formula
- [A1] (i) Obtain given answer
- [B1] (ii) Show correct sketch for one branch
- [B1] (ii) Both branches correct and nothing else seen in the interval
- [B1] (ii) Show asymptote at x = 45Y
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