Question

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

Answer 1

Explanation:

Given

To Prove

`(3\sin x)/(1-\cos x)=3\csc x+3\cot x`

Take the Left side of equation and rationalize

`\Rightarrow (3\sin x)/(1-\cos x)* (1+\cos x)/(1+\cos x)\\\\\Rightarrow (3\sin (1+\cos x))/(1-\cos^2 x)\\\\\Rightarrow (3\sin (1+\cos x))/(\sin^2 x)\\\\\Rightarrow (3\sin x)/(\sin ^2x)+(3\sin x\cos x)/(\sin^2 x)\\\\\Rightarrow (3)/(\sin x)+(3\cos x)/(\sin x)\\\\\Rightarrow 3\csc x+3\cot x`

Left side is equal to right side

Hence, proved