Question : If $\cot 2 {A}=\tan \left({A}-48^{\circ}\right)$, then what is the value of $A$?
Option 1: $36^{\circ}$
Option 2: $46^{\circ}$
Option 3: $42^{\circ}$
Option 4: $40^{\circ}$
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Correct Answer: $46^{\circ}$
Solution :
$\cot 2 {A}=\tan \left({A}-48^{\circ}\right)$
$⇒\tan(90^{\circ}- 2 {A})=\tan \left({A}-48^{\circ}\right)$
$⇒90^{\circ}- 2 {A}=A-48^{\circ}$
$⇒3 {A}= 138^{\circ}$
$\therefore {A}= 46^{\circ}$
Hence, the correct answer is $46^{\circ}$.
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