O-LevelAdditional MathematicsTrigonometry4037/22 · May/June 2011 · Q46 Marks
Prove that 1/(1 - sinx) - 1/(1 + sinx) = 2 tanx secx.
- (a)Prove that 1/(1 - sinx) - 1/(1 + sinx) = 2 tanx secx.[3]
- (b)An acute angle x is such that sinx = p. Given that sin 2x = 2sinx cosx, find an expression, in terms of p, for cosec 2x.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2011). The mark or mark type is shown in brackets.
- [1] (a) Expresses with common denominator: (1+sinx) - (1-sinx) / (1-sinx)(1+sinx)
- [1] (a) = 2 sin x / cos² x
- [1] (a) = 2 (sin x / cos x) (1 / cos x) = 2 tan x sec x (AG)
- [1] (b) cos x = √(1 - p²)
- [1] (b) cosec 2x = 1 / sin 2x
- [1] (b) = 1 / (2p√(1 - p²))
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →