Question 12:
--- 12(a) ---
12(a) | Uses appropriate trig identity to
form quadratic equation in single
trigonometrical term.
Condone
2 ( ±1±cosec2x ) +2cosec2x=1+4cosecx
Completes rigorous argument to
show the required result | 1.1a
2.1 | M1
R1 | 2cot2x+2cosec2x=1+4cosecx
2 ( cosec2x−1 ) +2cosec2x=1+4cosecx
4cosec2x−4cosecx−3=0
--- 12(b) ---
12(b) | Solves quadratic and
3
Obtains one of cosecx= or
2
1
cosecx=−
2
OE | 1.1b | B1 | 3
cosecx=
2
1
or cosecx=− reject
2
since cosecx ≥1
2
3 5
cot2 x= −1=
 
2 4
2 5
tanx=−
5
Since x is obtuse
Explains why their spurious
solution(s) is rejected referring to
the range of cosec or sine with
explicit comparison to ±1
May accept later rejection for
valid reason ie sq root of
negative
OE | 2.4 | E1F
Uses trig identity or right-angled
triangle/Pythagoras or given
equation
with their exact value
of cosec x or sin x to obtain an
exact value of tan x
value used must satisfy
cosecx ≥1 OE | 1.1a | M1
Completes rigorous argument to
find correct exact magnitude of
tan x
ACF | 2.1 | R1
Deduces tan x is negative.
May be seen anywhere without
contradiction by a positive final
answer. | 2.2a | B1
Total | 7
Q | Marking instructions | AO | Mark | Typical solution