CAIE P3 2017 June — Question 1 3 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2017
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicReciprocal Trig & Identities
TypeDouble angle with reciprocal functions
DifficultyStandard +0.3 This is a straightforward identity proof requiring conversion of reciprocal trig functions to sin/cos, algebraic manipulation, and recognition of the cos 2x double angle formula. It's slightly above average difficulty due to the reciprocal functions and multi-step algebra, but follows a standard proof pattern with no novel insight required.
Spec1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05l Double angle formulae: and compound angle formulae

1 Prove the identity \(\frac { \cot x - \tan x } { \cot x + \tan x } \equiv \cos 2 x\).

Question 1:
AnswerMarks Guidance
AnswerMark Guidance
Express the LHS in terms of either \(\cos x\) and \(\sin x\) or in terms of \(\tan x\)B1
Use PythagorasM1
Obtain the given answerA1
Total: 3
## Question 1:
| Answer | Mark | Guidance |
|--------|------|----------|
| Express the LHS in terms of either $\cos x$ and $\sin x$ or in terms of $\tan x$ | B1 | |
| Use Pythagoras | M1 | |
| Obtain the given answer | A1 | |
| **Total: 3** | | |

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1 Prove the identity $\frac { \cot x - \tan x } { \cot x + \tan x } \equiv \cos 2 x$.\\

\hfill \mbox{\textit{CAIE P3 2017 Q1 [3]}}