Standard +0.3 This is a trigonometric equation requiring factorization and substitution techniques. Students must rewrite tan θ as sin θ/cos θ, multiply through by cos θ, factor out sin θ, then solve both sin θ = 0 (rejected due to interval) and a quadratic in cos θ. While multi-step, these are standard A-level techniques with no novel insight required, making it slightly easier than average.
Solve the equation
$$\sin\theta\tan\theta + 2\sin\theta = 3\cos\theta \quad \text{where } \cos\theta \neq 0$$
Give all values of \(\theta\) to the nearest degree in the interval \(0° < \theta < 180°\)
Fully justify your answer. [5 marks]
Solve the equation
$$\sin\theta\tan\theta + 2\sin\theta = 3\cos\theta \quad \text{where } \cos\theta \neq 0$$
Give all values of $\theta$ to the nearest degree in the interval $0° < \theta < 180°$
Fully justify your answer. [5 marks]
\hfill \mbox{\textit{SPS SPS SM Pure 2021 Q12 [5]}}