Question

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

Hint: Use the information, $\tan 2A = \cot (A - {24^0})$ and solve carefully.
Consider the given equation, $\tan 2A = \cot (A - {24^0})$. We know that, $\tan \theta = \cot ({90^ \circ } - \theta )$.
$\tan 2A = \cot (A - {24^0}) \\ \Rightarrow \cot ({90^ \circ } - 2A) = \cot (A - {24^0}) \\ \Rightarrow {90^ \circ } - 2A = A - {24^0} \\ \Rightarrow 3A = {114^ \circ } \\ \Rightarrow A = {38^ \circ } \\$