Find tan(α+β).

01 / Standard#Your turn

0<\alpha,\beta<\frac\pi2,\quad\tan\alpha=\frac15,\quad\cos\beta=\frac{3\sqrt{13}}{13}

Official paper · jm01-2024 · II.2(a) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Use the acute-angle condition to find sinβ.

Hint 2

Apply the tangent addition formula.

Worked solution

Recover the other trigonometric ratios of β.
$\sin\beta=\frac{2\sqrt{13}}{13},\quad\tan\beta=2/3$
The denominator is nonzero.
$\tan(\alpha+\beta)=\frac{1/5+2/3}{1-(1/5)(2/3)}=1$

tan(α+β)=1.

Checks and common pitfalls: The tangent addition denominator has a minus sign.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Recover the other trigonometric ratios of β.
$\sin\beta=\frac{2\sqrt{13}}{13},\quad\tan\beta=2/3$
The denominator is nonzero.
$\tan(\alpha+\beta)=\frac{1/5+2/3}{1-(1/5)(2/3)}=1$

Think first. Reveal a hint when the class is ready.

2024 JM01