trigonometric problem

**mastermin346** · July 5th 2010, 07:01 AM

Given $tan\frac{A}{2}=\frac{1}{2}$ ,find the value of $cot A$

**Soroban** · July 5th 2010, 07:16 AM

hELLO, mastermin346!

We need two identities:

. . $\tan2\theta \:=\:\dfrac{2\tan\theta}{1 - \tan^2\!\theta}$

. . $\cot\theta \:=\:\dfrac{1}{\tan\theta}$

Given: $\tan\frac{A}{2}=\frac{1}{2}$ , find the value of $\cot A$

$\tan A \;=\;\dfrac{2\tan\frac{A}{2}}{1-\tan^2\!\frac{A}{2}} \;=\;\dfrac{2(\frac{1}{2})}{1 - (\frac{1}{2})^2} \;=\;\dfrac{1}{\frac{3}{4}} \;=\;\dfrac{4}{3}$

Therefore: . $\cot A \;=\;\dfrac{1}{\frac{4}{3}} \;=\;\dfrac{3}{4}$

**Mathelogician** · July 5th 2010, 07:17 AM

tan A= tan(2*A/2)=2tan(A/2)/[1-tan^2(A/2)]=4/3.
cot A=1/tan A=3/4.

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