Question

Prove or disprove that (1)/(1-cot x) is the same as (sin x)/(sin x - cos x)

Answer 1

$\dfrac{1}{1-\cot x}=\dfrac{\sin x}{\sin x-\cos x}\\\\L_s=\dfrac{1}{1-\dfrac{\cos x}{\sin x}}=\dfrac{1}{\dfrac{\sin x}{\sin x}-\dfrac{\cos x}{\sin x}}=\dfrac{1}{\dfrac{\sin x-\cos x}{\sin x}}=\dfrac{\sin x}{\sin x-\cos x}=R_s$

$\text{Used:}\\\\\cot x=\dfrac{\cos x}{\sin x}$