Prove that ((sinθ + cosθ)²-1)/(cos²θ) ≡ 2 tanθ.

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2024). The mark or mark type is shown in brackets.

1. [M1] Expand bracket to obtain 3 terms and use correct identity θ may be missing or another symbol used.
2. [M1] Use identity sinθ/cosθ = tanθ Does not require any further explanation. θ may be missing or another symbol used.
3. [A1] Conclude with 2tanθ WWW AG
4. [M1] Attempt solution of 5tan³θ=2tanθ to obtain at least one value of tanθ Can be awarded if tanθ is cancelled and ignored.
5. [A1] Obtain at least two of 0, ±32.3 Or greater accuracy. SC B1 if no method shown.
6. [A1] Obtain all three values Or greater accuracy; and no others in −90°<θ<90° range. Other units SC B1 only for all 3 angles. SC B1 if no method shown.