Showing all necessary working, solve the equation sec α cosec α = 7 for 0° < α < 90°.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

1. [B1] Express equation as (1 / (cos α sin α)) = 7 OE; May be implied by subsequent work
2. [M1] Attempt use of identity for sin 2α or attempt to obtain a quadratic equation in terms of any one of the following: sin² α, cos² α, cot² α or tan² α From equation of form sin2α=k_where 0<k<1or from use of correct identities
3. [A1] Obtain sin 2α = 2/7 or a correct 3 term quadratic equation, equated to zero in any one of the following: sin² α, cos² α, cot² α or tan² α
4. [M1] Attempt correct process to find at least one correct value of α
5. [A1] Obtain 8.3 and 81.7 and no others between 0 and 90
6. [B1] Simplify left-hand side to obtain 2 sin β cos 20°
7. [M1] Attempt to form equation where tan β is only variable, tan β ≠ 3
8. [A1] Obtain tan β = (3 / cos 20°) OE
9. [A1] Obtain β = 72.6 and no others between 0 and 90