tan ( - pie / 12 ) =
- tan ( pie / 12 ) =
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Remainder formula :
tan^2 (x) = [ 1 - 2Cos(2x) ] ÷ [ 1 + 2Cos(2x) ]
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Thus :
tan^2 ( pie/12) =
[ 1 - Cos( 2pie/12 ) ] ÷ [ 1 + Cos( 2pie/12 ) ] =
[ 1 - Cos( pie/6 ) ] ÷ [ 1 + Cos( pie/6 ) ] =
[ 1 - √3/2 ] ÷ [ 1 + √3/2 ] =
[ 2 - √3 / 2 ] ÷ [ 2 + √3 / 2 ] =
[ 2 - √3 ] ÷ [ 2 + √3 ] =
2 - √3 / 2 + √3 =
(2 - √3)(2 - √3) / (2 + √3)(2 - √3) =
(2 - √3)^2 / 4 - 3 =
(2 - √3)^2 / 1 =
(2 - √3)^2
So :
tan^2 ( pie/12 ) = (2 - √3)^2
Take a square root from both sides
tan( pie/12 ) = 2 - √3
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Thus ;
- tan ( pie/12 ) = - ( 2 - √3 )
- tan ( pie/12 ) = - 2 + √3
Approximately :
- tan ( pie/12 ) = - 2 + 1.732
- tan ( pie/12 ) = - 0.268
