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Find the value of A if $\tan 2A = \cot (A - {24^0})$.

Answer
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Hint: Use the information, $\tan 2A = \cot (A - {24^0})$ and solve carefully.

Complete step-by-step answer:
Consider the given equation, $\tan 2A = \cot (A - {24^0})$. We know that, $\tan \theta = \cot ({90^ \circ } - \theta )$.

Using this formula in the given equation,
$
  \tan 2A = \cot (A - {24^0}) \\
   \Rightarrow \cot ({90^ \circ } - 2A) = \cot (A - {24^0}) \\
   \Rightarrow {90^ \circ } - 2A = A - {24^0} \\
   \Rightarrow 3A = {114^ \circ } \\
   \Rightarrow A = {38^ \circ } \\
$

Note: It’s always better to learn and understand the formulas. Especially in trigonometry. In trigonometry, if we talk about problem solving then formulas play a vital role in that.