Question

Choose the correct answers from the alternatives given.
If $\frac{2sin\theta -cos\theta }{cos\theta +sin\theta }$ = 1 , then value of cot $\theta$ is

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. 3
• D. 2

Answer 1

Answer: (A)

$\frac{1}{2}$

$\frac{2sin\theta -cos\theta }{cos\theta +sin\theta }=1$
$\frac{sin\theta (2-\frac{cos\theta }{sin\theta })}{sin\theta (\frac{cos\theta }{sin\theta }+1)}=1$
$\frac{2-cot\theta }{cot\theta +1}$
$2-1=cot\theta$
Hence, $cot\theta =\frac{1}{2}$