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

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Question 1117821: Evaluate tan%28x-pi%2F6%29 if cot%28x%29=1%2F2



Thank you!
Found 2 solutions by ikleyn, stanbon:
Answer by ikleyn(52863) About Me  (Show Source):
You can put this solution on YOUR website!
.

There is nothing easier. 

Since cot(x) = 1%2F2, then tan(x) = 2.


Next,  tan%28x-pi%2F6%29 = apply the formula for the tan of difference = 


= %28tan%28x%29-tan%28pi%2F6%29%29%2F%281+%2B+tan%28x%29%2Atan%28pi%2F6%29%29 = now substitute tan(x) = 2,  tan%28pi%2F6%29 = sqrt%283%29%2F3  to get 


= %282-sqrt%283%29%2F3%29%2F%281%2B2%2A%28sqrt%283%29%2F3%29%29 = %286-sqrt%283%29%29%2F%283%2B2%2Asqrt%283%29%29 = %286-sqrt%283%29%29%2F%283%2B2%2Asqrt%283%29%29.%283-2%2Asqrt%283%29%29%2F%283-2%2Asqrt%283%29%29 =  = %2824-15%2Asqrt%283%29%29%2F%28-3%29 = -8+%2B+5%2Asqrt%283%29 = 0.66 (approximately).

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The answer and the solution by  @stanbon  are incorrect.



Answer by stanbon(75887) About Me  (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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