| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Trig Proofs |
| Type | Prove trigonometric identity |
| Difficulty | Moderate -0.8 Part (a) is a straightforward trigonometric identity proof requiring only the substitution tan x = sin x/cos x and basic algebraic manipulation. Part (b) is a routine trigonometric equation solved by using the Pythagorean identity and basic algebra. Both parts are standard textbook exercises with no problem-solving insight required, making this easier than average. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}[label=(\alph*)]
\item Prove that $\cos x + \sin x \tan x \equiv \frac{1}{\cos x}$ (where $x \neq \frac{1}{2}n\pi$ for any odd integer $n$). [3]
\item Solve the equation $2\sin^2 x = \cos^2 x$ for $0° \leqslant x \leqslant 180°$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q1 [5]}}