Standard +0.3 Part (i) is a straightforward application of the double angle formula cos(2x) = 2cos²(x) - 1 with simple algebraic manipulation involving surds. Part (ii) requires expanding compound angle formulae and solving for tan(y), which is slightly more involved but still follows standard procedures. Both parts are routine C3-level exercises with no novel problem-solving required, making this slightly easier than average.
4. (i) Given that \(\cos x = \sqrt { 3 } - 1\), find the value of \(\cos 2 x\) in the form \(a + b \sqrt { 3 }\), where \(a\) and \(b\) are integers.
(ii) Given that
$$2 \cos ( y + 30 ) ^ { \circ } = \sqrt { 3 } \sin ( y - 30 ) ^ { \circ }$$
find the value of \(\tan y\) in the form \(k \sqrt { 3 }\) where \(k\) is a rational constant.
4. (i) Given that $\cos x = \sqrt { 3 } - 1$, find the value of $\cos 2 x$ in the form $a + b \sqrt { 3 }$, where $a$ and $b$ are integers.\\
(ii) Given that
$$2 \cos ( y + 30 ) ^ { \circ } = \sqrt { 3 } \sin ( y - 30 ) ^ { \circ }$$
find the value of $\tan y$ in the form $k \sqrt { 3 }$ where $k$ is a rational constant.\\
\hfill \mbox{\textit{OCR C3 Q4 [8]}}