| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Reciprocal Trig & Identities |
| Type | Solve equation using Pythagorean identities |
| Difficulty | Standard +0.3 Part (a) is a standard identity derivation by dividing through by cos²θ. Part (b) requires substituting the identity to form a quadratic in secθ, then solving—a routine multi-step C3 question with no novel insight required, slightly easier than average due to straightforward algebraic manipulation. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^21.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}
\item (a) Given that $\sin ^ { 2 } \theta + \cos ^ { 2 } \theta \equiv 1$, show that $1 + \tan ^ { 2 } \theta \equiv \sec ^ { 2 } \theta$.\\
(b) Solve, for $0 \leq \theta < 360 ^ { \circ }$, the equation
\end{enumerate}
$$2 \tan ^ { 2 } \theta + \sec \theta = 1 ,$$
giving your answers to 1 decimal place.\\
\hfill \mbox{\textit{Edexcel C3 Q1 [8]}}