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# If tan 2A = cot (A - 18^o) where 2A is an acute angle find the value of A.

3. If  $\tan 2A= \cot (A-18^{o})$, where $2A$ is an acute angle, find the value of $A$.

Views

We have,
$\tan$ 2A  = $\cot$ (A - $\18^{0}$
we know that, $\\\cot (90^0-\theta) = \tan\theta$
$\\\Rightarrow \cot (90^0-2A) = \cot (A-18^0)\\\Rightarrow 90^0-2A = A - 18^0\\\Rightarrow 3A = 108\\\Rightarrow A = 108/3 = 36^0$

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