Mathematics 9709 · AS & A Level · Trigonometry

Trigonometry — practice question

The angle $\alpha$ is between $0^{\circ}$ and $90^{\circ}$, and it satisfies $2\tan^{2}\alpha + \sec^{2}\alpha = 5 - 4\tan\alpha$.

(i)[4]

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

(ii)[5]

Given that $\beta$ satisfies $\cot(\alpha + \beta) = 6$, find the exact value of $\cot\beta$ without using a calculator.

Worked solution & mark scheme

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