Question

If \(\frac {(2 sin\ θ – cos\ θ)}{(cos\ θ + sin\ θ)} = 1\), then the value of \(cot\ θ \) is

• A. \(\frac 12\)
• B. \(\frac 13\)
• C. \(3\)
• D. \(2\)

Answer 1

The Correct Option is A

To find the value of \(\cot \theta\) given \(\frac{(2 \sin \theta - \cos \theta)}{(\cos \theta + \sin \theta)} = 1\), we start by equating the given expression to 1:

\(\frac{2 \sin \theta - \cos \theta}{\cos \theta + \sin \theta} = 1\) 

Cross-multiplying gives us:

\(2 \sin \theta - \cos \theta = \cos \theta + \sin \theta\)

Rearrange terms to isolate sine and cosine terms:

\(2 \sin \theta - \sin \theta = \cos \theta + \cos \theta\)

Simplify to:

\(\sin \theta = 2 \cos \theta\)

We know that \(\cot \theta = \frac{\cos \theta}{\sin \theta}\). Substitute \(\sin \theta = 2 \cos \theta\):

\(\cot \theta = \frac{\cos \theta}{2 \cos \theta}\)

Simplify to find:

\(\cot \theta = \frac{1}{2}\)

Therefore, the value of \(\cot \theta\) is \(\frac{1}{2}\).