Standard +0.3 This is a straightforward two-part trigonometric equation question. Part (i) requires routine manipulation using tan θ = sin θ/cos θ and the Pythagorean identity to reach a quadratic in cos θ—a standard technique. Part (ii) applies the result with a simple substitution (θ = 3x) and solving for x in the given range. The question is slightly above average due to the multi-step algebraic manipulation, but follows a well-practiced pattern with no novel insight required.
8. (i) Given that \(6 \tan \theta \sin \theta = 5\), show that \(6 \cos ^ { 2 } \theta + 5 \cos \theta - 6 = 0\).
(3 marks)
(ii) Hence solve the equation \(6 \tan 3 x \sin 3 x = 5\), giving all values of \(x\) to the nearest degree in the interval \(0 ^ { \circ } \leqslant x \leqslant 180 ^ { \circ }\).
(2 marks)
8. (i) Given that $6 \tan \theta \sin \theta = 5$, show that $6 \cos ^ { 2 } \theta + 5 \cos \theta - 6 = 0$.\\
(3 marks)\\
(ii) Hence solve the equation $6 \tan 3 x \sin 3 x = 5$, giving all values of $x$ to the nearest degree in the interval $0 ^ { \circ } \leqslant x \leqslant 180 ^ { \circ }$.\\
(2 marks)\\
\hfill \mbox{\textit{SPS SPS SM Pure 2021 Q8 [5]}}