| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2025 |
| Session | February |
| Marks | 8 |
| Topic | Standard trigonometric equations |
| Type | Deduce related solution |
| Difficulty | Standard +0.3 Part (a) requires standard trigonometric manipulation using tan x = sin x/cos x and the Pythagorean identity, which is routine A-level technique. Part (b) applies the result with a double angle substitution and requires careful consideration of the range, adding modest problem-solving demand. Overall slightly easier than average due to the guided structure and standard methods. |
| 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 Show that the equation
$$2 \sin x \tan x = \cos x + 5$$
can be expressed in the form
$$3 \cos^2 x + 5 \cos x - 2 = 0.$$ [3]
\item Hence solve the equation
$$2 \sin 2\theta \tan 2\theta = \cos 2\theta + 5,$$
giving all values of $\theta$ between $0°$ and $180°$, correct to $1$ decimal place. [5]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2025 Q7 [8]}}