Mathematics 9709 · AS & A Level · Trigonometry

Trigonometry — practice question

For an angle $\alpha$ between $0^\circ$ and $90^\circ$, it is given that $2\tan^2 \alpha + \sec^2 \alpha = 5 - 4\tan \alpha$.

(i)[4]

Show that $3\tan^2 \alpha + 4\tan \alpha - 4 = 0$ and then determine the exact value of $\tan \alpha$.

(ii)[5]

The angle $\beta$ is given such that $\cot(\alpha + \beta) = 6$. Without a calculator, determine the exact value of $\cot \beta$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply $\sec^2\alpha = 1 + \tan^2\alpha$” …