How do you use a half-angle formula to simplify $tan 75$ ?

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Answer 1 · 2015-05-27T01:42:26

$tan(75^@) = tan((150^@)/2) = (1-cos(150^@))/sin(150^2)$

The reference angle for $150^@$ is $30^@$
and $150^@$ is in quadrant 2 so
$cos(150^@)$ is negative and #sin(150^@) is positive.

That is $tan(75^@)$

$=(1-cos(150^@))/(sin(150^@))$

$= (1+cos(30^@))/(sin(30^@))$

$= (1+sqrt(3) /2)/(1/2)$

$= 2 + sqrt(3)$

How do you use a half-angle formula to simplify tan 75tan 75?