(a)[3]
Show that the expression $\sec^4 \theta - \tan^4 \theta$ is equal to $1 + 2\tan^2 \theta$.
(b)[5]
For $0^\circ < \alpha < 180^\circ$, hence or otherwise solve the equation $\sec^4 2\alpha - \tan^4 2\alpha = 2\tan^2 2\alpha \, \sec^2 2\alpha$.
Mathematics 9709 · AS & A Level · Trigonometry
Trigonometry — practice question
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Obtain a factorised form, or an expression in $\cos^2\theta$ or $\sec^2\theta$.” …
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