(a)[3]
Show, using identities, that $\tan^4\theta-1\equiv\frac{1-2\cos^2\theta}{\cos^4\theta}$.
(b)[4]
Hence, solve the equation $\cos^2\theta(\tan^4\theta-1)=7$ for $0^\circ<\theta<180^\circ$.
Mathematics 9709 · AS & A Level · Trigonometry
Trigonometry — practice question
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply $\tan^4\theta=\frac{\sin^4\theta}{\cos^4\theta}$ or a matching identity” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI