OCR MEI C4 — Question 1 6 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicReciprocal Trig & Identities
TypeSolve equation using Pythagorean identities
DifficultyModerate -0.3 This question requires knowledge of the standard trigonometric identity cosec²θ = 1 + cot²θ, followed by solving a straightforward quadratic equation in cot θ and finding angles. It's a routine multi-step problem testing identity manipulation and equation solving, slightly easier than average due to the direct substitution and standard quadratic factorization involved.
Spec1.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^21.05o Trigonometric equations: solve in given intervals

Given that \(\cosec^2 \theta - \cot \theta = 3\), show that \(\cot^2 \theta - \cot \theta - 2 = 0\). Hence solve the equation \(\cosec^2 \theta - \cot \theta = 3\) for \(0° \leqslant \theta \leqslant 180°\). [6]

Given that $\cosec^2 \theta - \cot \theta = 3$, show that $\cot^2 \theta - \cot \theta - 2 = 0$.

Hence solve the equation $\cosec^2 \theta - \cot \theta = 3$ for $0° \leqslant \theta \leqslant 180°$. [6]

\hfill \mbox{\textit{OCR MEI C4  Q1 [6]}}