Step-by-step explanation:
Given
To Prove
[tex]\dfrac{3\sin x}{1-\cos x}=3\csc x+3\cot x[/tex]
Take the Left side of equation and rationalize
[tex]\Rightarrow \dfrac{3\sin x}{1-\cos x}\times \dfrac{1+\cos x}{1+\cos x}\\\\\Rightarrow \dfrac{3\sin (1+\cos x)}{1-\cos^2 x}\\\\\Rightarrow \dfrac{3\sin (1+\cos x)}{\sin^2 x}\\\\\Rightarrow \dfrac{3\sin x}{\sin ^2x}+\dfrac{3\sin x\cos x}{\sin^2 x}\\\\\Rightarrow \dfrac{3}{\sin x}+\dfrac{3\cos x}{\sin x}\\\\\Rightarrow 3\csc x+3\cot x[/tex]
Left side is equal to right side
Hence, proved
