| Exam Board | SPS |
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| Module | SPS FM Pure (SPS FM Pure) |
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| Year | 2025 |
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| Session | June |
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| Topic | Product & Quotient Rules |
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4. Given that
$$y = \frac { 3 \sin \theta } { 2 \sin \theta + 2 \cos \theta } \quad - \frac { \pi } { 4 } < \theta < \frac { 3 \pi } { 4 }$$
show that
$$\frac { \mathrm { d } y } { \mathrm {~d} \theta } = \frac { A } { 1 + \sin 2 \theta } \quad - \frac { \pi } { 4 } < \theta < \frac { 3 \pi } { 4 }$$
where \(A\) is a rational constant to be found.
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