Question

If $\cot \theta +\csc \theta =2$, then the value of $\frac{1+\cos \theta }{1-\cos \theta }$ is

• A. $2$
• B. $4$
• C. $\frac{1}{2}$
• D. $\frac{1}{4}$

Answer 1

Answer: (B)

$4$

$\cot \theta +\csc \theta =2$ .....(1)
${\csc }^2\theta -{\cot }^2\theta =1$
$\csc \theta -\cot \theta =\frac{1}{2}$ ......(2)
adding (1) & (2)
$2\csc \theta =\frac{5}{2}$
$\csc \theta =\frac{5}{4}$
$\cos \theta =\frac{3}{5}$
$\frac{1+\cos \theta }{1-\cos \theta }=\frac{1+\frac{3}{5}}{1-\frac{3}{5}}=\frac{8}{2}=4$