OCR MEI C4 — Question 2 4 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicReciprocal Trig & Identities
TypeSolve equation using Pythagorean identities
DifficultyStandard +0.3 This is a straightforward application of the Pythagorean identity cosec²x = 1 + cot²x to transform the equation into a simple quadratic in cot x, followed by routine inverse trig to find solutions. While it requires knowledge of reciprocal trig identities, the algebraic manipulation is minimal and the solution method is standard textbook fare, making it slightly easier than average.
Spec1.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^21.05o Trigonometric equations: solve in given intervals
2 Solve the equation \(3 \operatorname { cosec } ^ { 2 } x = 2 \cot ^ { 2 } x + 3\) for values of \(x\) in the range \(0 ^ { \circ } < x < 360 ^ { \circ }\).
Question 2:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(3\cosec^2 x = 2\cot^2 x + 3\)M1 Use identity
\(\Rightarrow 3(1 + \cot^2 x) = 2\cot^2 x + 3\)A1
\(\Rightarrow \cot^2 x = 0\)
\(\Rightarrow \cot x = 0\)A1
\(\Rightarrow x = 90°\) or \(270°\)A1 One for each angle
Total: 4 marks 
## Question 2:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $3\cosec^2 x = 2\cot^2 x + 3$ | M1 | Use identity |
| $\Rightarrow 3(1 + \cot^2 x) = 2\cot^2 x + 3$ | A1 | |
| $\Rightarrow \cot^2 x = 0$ | | |
| $\Rightarrow \cot x = 0$ | A1 | |
| $\Rightarrow x = 90°$ or $270°$ | A1 | One for each angle |
| **Total: 4 marks** | | |

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2 Solve the equation $3 \operatorname { cosec } ^ { 2 } x = 2 \cot ^ { 2 } x + 3$ for values of $x$ in the range $0 ^ { \circ } < x < 360 ^ { \circ }$.

\hfill \mbox{\textit{OCR MEI C4  Q2 [4]}}
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