Question

HELP! NOW! Prove the trig identity: 3sinx/1-cosx=3cscx+3cotx

Answer 1

Step-by-step explanation:

Given

To Prove

$\dfrac{3\sin x}{1-\cos x}=3\csc x+3\cot x$

Take the Left side of equation and rationalize

$\Rightarrow \dfrac{3\sin x}{1-\cos x}\times \dfrac{1+\cos x}{1+\cos x}\\\\\Rightarrow \dfrac{3\sin (1+\cos x)}{1-\cos^2 x}\\\\\Rightarrow \dfrac{3\sin (1+\cos x)}{\sin^2 x}\\\\\Rightarrow \dfrac{3\sin x}{\sin ^2x}+\dfrac{3\sin x\cos x}{\sin^2 x}\\\\\Rightarrow \dfrac{3}{\sin x}+\dfrac{3\cos x}{\sin x}\\\\\Rightarrow 3\csc x+3\cot x$

Left side is equal to right side

Hence, proved