Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
• cscx = [tex]\frac{1}{sinx}[/tex]
• cot²x = [tex]\frac{cos^2x}{sin^2x}[/tex], sin²x + cos²x = 1
Consider the left side
cscx - sinx
= [tex]\frac{1}{sinx}[/tex] - sinx
=[tex]\frac{1-sin^2x}{sinx}[/tex]
= [tex]\frac{cos^2x}{sinx}[/tex] × [tex]\frac{sinx}{sinx}[/tex]
= [tex]\frac{cos^2x}{sin^2x}[/tex] × sinx
= cot²x × [tex]\frac{1}{cscx}[/tex]
= [tex]\frac{cot^2x}{cscx}[/tex] = right side ⇒ verified
