Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
• cot x = [tex]\frac{cosx}{sinx}[/tex]
• sec x = [tex]\frac{1}{cosx}[/tex] and cosec x = [tex]\frac{1}{sinx}[/tex]
Consider the left side
[tex]\frac{cotx}{secx}[/tex]
= [tex]\frac{cosx}{sinx}[/tex] × cosx
= [tex]\frac{cos^2x}{sinx}[/tex]
= [tex]\frac{1-sin^2x}{sinx}[/tex]
= [tex]\frac{1}{sinx}[/tex] - [tex]\frac{sin^2x}{sinx}[/tex]
= cosec x - sin x
= right side ⇒ verified
