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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