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

Sagot :

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

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