Standard +0.3 Part (i) requires implicit differentiation with a trigonometric function and algebraic manipulation using trig identities, which is standard C4 material. Part (ii) is a routine chain rule application to find a tangent equation. Both parts are straightforward applications of techniques with no novel problem-solving required, making this slightly easier than average.
5. (i) Given that
$$x = \sec \frac { y } { 2 } , \quad 0 \leq y < \pi$$
show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 } { x \sqrt { x ^ { 2 } - 1 } }$$
(ii) Find an equation for the tangent to the curve \(y = \sqrt { 3 + 2 \cos x }\) at the point where \(x = \frac { \pi } { 3 }\).
5. (i) Given that
$$x = \sec \frac { y } { 2 } , \quad 0 \leq y < \pi$$
show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 } { x \sqrt { x ^ { 2 } - 1 } }$$
(ii) Find an equation for the tangent to the curve $y = \sqrt { 3 + 2 \cos x }$ at the point where $x = \frac { \pi } { 3 }$.\\
\hfill \mbox{\textit{OCR C4 Q5 [9]}}