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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.

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.

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