Simplify the expression by using a double angle formula2 tan 18 degrees/ 1-tan^2 18 degrees

Grethe asked Nov 3, 2023

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Grethe asked Nov 3, 2023

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11 votes

Given the expression:

$(2\tan18\degree)/(1-\tan^218\degree)$

Using the double angle formula for the tangent:

$\tan(2x)=(2\tan x)/(1-\tan^2x)$

Finally, we identify x = 18°:

$(2\tan18\degree)/(1-\tan^218\degree)=\tan36\degree$

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