O-LevelAdditional MathematicsTrigonometry4037/21 · May/June 2024 · Q108 Marks
Show that (tanx+secx)² can be written as (1+sinx)/(1-sinx).
- (a)Show that (tanx+secx)² can be written as (1+sinx)/(1-sinx).[4]
- (b)Hence solve the equation (tan 3θ+sec3θ)² = 6 for 0° < θ≤ 180°.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.
- [M1] tan²x + 2tanxsecx + sec²x or (sinx/cosx + 1/cosx)²
- [A1] (sin²x/cos²x) + (2sinx/cos²x) + (1/cos²x) or (sinx+1)²/cos²x
- [A1] (1+sinx)² / (1-sin²x)
- [A1] (1+sinx)(1+sinx) / (1-sinx)(1+sinx) = (1+sinx)/(1-sinx) (must be fully justified)
- [B1] 7sin3θ = 5
- [M1] One correct value for 3θ soi e.g. 45.58... 134.4... 405.5... 494.4...
- [A2] 15.2 or 44.8 or 135.2 or 164.8 (with no extras in range)
- [A1] for any 2 correct, ignoring extras
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