Question : If $\frac{2 \sin A-\cos A}{\sin A+\cos A}=1$, then find the value of $\cot A$.
Option 1: $1$
Option 2: $\frac{1}{2}$
Option 3: $\frac{1}{3}$
Option 4: $2$
Correct Answer: $\frac{1}{2}$
Solution : Given, $\frac{2 \sin A-\cos A}{\sin A+\cos A}=1$ Taking $\sin A$ as common ⇒ $\frac{\sin A(2-\frac{\cos A}{\sin A})}{\sin A(1+\frac{\cos A}{\sin A})}=1$ ⇒ $2-\cot A=1+\cot A$ ⇒ $2\cot A = 1$ ⇒ $\cot A = \frac12$ Hence, the correct answer is $\frac12$.
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