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A and B are acute angles with tan A = 1/2 and tan B = 1/3.

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$A$ and $B$ are acute angles with $\tan A = \dfrac{1}{2}$ and $\tan B = \dfrac{1}{3}$ . Show that $A + B = \dfrac{\pi}{4}$ , and give $A + B$ in degrees.

Need a reminder? The key ideaShow

$\cos(x \pm y) = \cos x \cos y \mp \sin x \sin y$ and $\sin(x \pm y) = \sin x \cos y \pm \cos x \sin y$ . Dividing gives $\tan(x \pm y) = \dfrac{\tan x \pm \tan y}{1 \mp \tan x \tan y}$ . The quadrant of each angle gives the sign of each ratio.

The worked solution

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A and B are acute angles with tan A = 1/2 and tan B = 1/3.

The worked solution

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