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Prove that tan(π/4 + x) = (1 + tan x)/(1 - tan x).

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Prove that $\tan\left(\dfrac{\pi}{4} + x\right) = \dfrac{1 + \tan x}{1 - \tan x}$ . Use it to find the exact value of $\tan 75^\circ$ , and give it to three decimal places.

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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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

← All Problems

← sin A = 4/5 with π/2 < A < π, and cos B = -5/13 with π < B < 3π/2.A and B are acute angles with tan A = 1/2 and tan B = 1/3. →

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Prove that tan(π/4 + x) = (1 + tan x)/(1 - tan x).

The worked solution

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