MediumMathematicsHigh School (11–12)Trigonometry › Compound and Multiple Angles Trigonometry › Trigonometric IdentitiesproofBoard Exam A-Level IB

Prove that (1 - cos 2x + sin 2x)/(1 + cos 2x + sin 2x) = 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 $\dfrac{1 - \cos 2x + \sin 2x}{1 + \cos 2x + \sin 2x} = \tan x$ .

Need a reminder? The key ideaShow

$\sin 2x = 2\sin x \cos x$ ; $\cos 2x = \cos^2 x - \sin^2 x = 2\cos^2 x - 1 = 1 - 2\sin^2 x$ ; $\tan 2x = \dfrac{2\tan x}{1 - \tan^2 x}$ . Triple angles: $\sin 3x = 3\sin x - 4\sin^3 x$ and $\cos 3x = 4\cos^3 x - 3\cos x$ .

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.

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Prove that (1 - cos 2x + sin 2x)/(1 + cos 2x + sin 2x) = tan x.

The worked solution

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