SOLUTION: Evaluate {{{tan(x-pi/6)}}} if {{{cot(x)=1/2}}} Thank you!

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Question 1117821: Evaluate if



Thank you!
Found 2 solutions by ikleyn, stanbon:
Answer by ikleyn(52873)   (Show Source): You can put this solution on YOUR website!
.

There is nothing easier. 

Since cot(x) = , then tan(x) = 2.


Next,   = apply the formula for the tan of difference = 


=  = now substitute tan(x) = 2,   =   to get 


=  =  = . =  =  =  = 0.66 (approximately).

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The answer and the solution by  @stanbon  are incorrect.



Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Evaluate tan(x-pi/6) if cot(x)=1/2
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Note:: tan(x) = 2
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tan(x-pi/6) = [tan(x)-tan(pi/6)]/[1-tan(x)*tan(pi/6)]
= [2-(1/sqrt(3)]/[1-2*(1/sqrt(3)]
= [(2sqrt(3)-1)/sqrt(3)]/[(sqrt(3)-2)/sqrt(3)]
= [2sqrt(3)-1]/[sqrt(3)-2]
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Cheers,
Stan H.
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