Solve the equation sinα cosec²α + cosα sec²α = 0 for -π < α < π, where α is in radians.

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

1. [1] B1 For dealing correctly with cosec²α and sec²α to obtain an expression in sinα and cosα only
2. [1] B1 For an equation in tanα, may be implied by a correct solution.
3. [1] B1 for one correct solution
4. [1] B1 for a second correct solution and no extra solutions in the range.
5. [1] M1 For dealing with the fractions correctly and expansion of (1 − sinθ)²
6. [1] M1 Dep for use of identity, may be implied by 2(1-sinθ)/cosθ(1-sinθ)
7. [1] M1 Dep on previous M mark for simplification
8. [1] A1 Need to see this detail for A1 Need to have had θ in every trigonometric ratio.
9. [1] B1 cos3φ = 1/2
10. [1] M1 for one correct solution of their cos 3θ = k using a correct order of operations
11. [1] A1 for 2 correct solutions
12. [1] A1 for a third correct solution with no extra solutions in the range