Question

The value of $\frac{\cot \Theta +cosec\Theta -1}{\cot \Theta -cosec\Theta +1}$ is

• A. $\frac{1+\cos \Theta }{\sin \Theta }$
• B. $\frac{1+\sin \Theta }{\sin \Theta }$
• C. $\frac{1-\cos \Theta }{\sin \Theta }$
• D. $\frac{1-\sin \Theta }{\sin \Theta }$

Answer 1

The correct option is A $\frac{1+\cos \Theta }{\sin \Theta }$

$cot\theta =\frac{cos\theta }{sin\theta }$ and $cosec\theta =\frac{1}{sin\theta }$
$\frac{cot\theta +cosec\theta -1}{cot\theta -cosec\theta +1}=\frac{\frac{cos\theta }{sin\theta }+\frac{1}{sin\theta }-1}{\frac{cos\theta }{sin\theta }-\frac{1}{sin\theta }+1}$
$\Rightarrow \frac{cos\theta +1-sin\theta }{cos\theta -1+sin\theta }=$