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: $2$
Answer (1)
24th Jan, 2024
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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