A-LevelMathematicsTrigonometry9709/12 · Oct/Nov 2020 · Q66 Marks
Prove the identity ( 1 COS X – tan x )( 1 sin x + 1 ) ≡ 1 tan x
- (a)Prove the identity ( 1 COS X – tan x )( 1 sin x + 1 ) ≡ 1 tan x[4]
- (b)Hence solve the equation ( 1 COS X – tan x )( 1 sin x + 1 ) = 2 tan²x for 0° ≤ x ≤ 180°.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [B1] Uses "tanx = sinx ÷ cosx" throughout
- [M1] Correct algebra leading to two or four terms
- [A1] OE. A correct expression which can be cancelled directly to cosx/sinx e.g. (cosx(1-sin²x))/(sinx(1-sin²x))
- [A1] AG. Must show cancelling. If x is missing throughout their working withhold this mark.
- [M1] Reducing to tan³x = k.
- [A1] (x =) 38.4° AWRT. Ignore extra answers outside the range 0 to 180° but A0 if within.
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