Question : If $\frac{(3 \sin \theta-\cos \theta)}{(\cos \theta+\sin \theta)}=1$, then the value of $\cot \theta$ is:
Option 1: 3
Option 2: 0
Option 3: 1
Option 4: 2
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Correct Answer: 1
Solution :
$\frac{(3 \sin \theta-\cos \theta)}{(\cos \theta+\sin \theta)}=1$
Divide the numerator and denominator by $\sin \theta$.
${(3 -\cot \theta)}={(\cot \theta+ 1)}$
⇒ $2\cot \theta = 2$
⇒ $\cot \theta=1$
Hence, the correct answer is 1.
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