Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
• sin²x + cos²x = 1
• cot x = [tex]\frac{cosx}{sinx}[/tex], csc x = [tex]\frac{1}{sinx}[/tex]
Consider the left side
[tex]\frac{1+cosx}{1-cosx}[/tex] - [tex]\frac{1-cosx}{1+cosx}[/tex]
Expressing as a single fraction
= [tex]\frac{(1+cosx)^2-(1-cosx)^2}{(1-cosx)(1+cosx)}[/tex]
Expand and simplify numerator/ denominator
= [tex]\frac{1+2cosx+cos^2x-1+2cosx-cos^2x}{1-cos^2x}[/tex]
= [tex]\frac{4cosx}{sin^2x}[/tex]
= [tex]\frac{4cosx}{sinx}[/tex] × [tex]\frac{1}{sinx}[/tex]
= 4cotxcscx = right side ⇒ verified
