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Write tan x in terms of cos x

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Answer to a math question Write tan x in terms of cos x

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Gene
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We know that \tan x = \frac{\sin x}{\cos x} .

Using trigonometric identity \sin^2 x + \cos^2 x = 1 , we can write \sin^2 x = 1 - \cos^2 x .

Therefore, \tan x = \frac{\sin x}{\cos x} = \frac{\sqrt{1-\cos^2 x}}{\cos x} .

Thus, \boxed{\tan x = \sqrt{\frac{1-\cos^2 x}{\cos^2 x}}} is \tan x in terms of \cos x .

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