Standard +0.3 This is a standard C3 reciprocal trig equation requiring the Pythagorean identity tan²x = sec²x - 1 to form a quadratic in sec x, then solving and finding angles. It's slightly above average difficulty due to the algebraic manipulation and multiple solutions in the given interval, but follows a well-practiced technique with clear scaffolding ('forming and solving a quadratic').
4 By forming and solving a quadratic equation, solve the equation
$$8 \sec x - 2 \sec ^ { 2 } x = \tan ^ { 2 } x - 2$$
in the interval \(0 < x < 2 \pi\), giving the values of \(x\) in radians to three significant figures.
4 By forming and solving a quadratic equation, solve the equation
$$8 \sec x - 2 \sec ^ { 2 } x = \tan ^ { 2 } x - 2$$
in the interval $0 < x < 2 \pi$, giving the values of $x$ in radians to three significant figures.
\hfill \mbox{\textit{AQA C3 2013 Q4 [7]}}