Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
• sec x = [tex]\frac{1}{cosx}[/tex], csc x = [tex]\frac{1}{sinx}[/tex]
• cot x = [tex]\frac{cosx}{sinx}[/tex]
Consider the left side
sec²x. cot²x - cos²x. csc²x
= [tex]\frac{1}{cos^2x}[/tex] × [tex]\frac{cos^2x}{sin^2x}[/tex] - cos²x × [tex]\frac{1}{sin^2x}[/tex]
= [tex]\frac{1}{sin^2x}[/tex] - [tex]\frac{cos^2x}{sin^2x}[/tex]
= [tex]\frac{1-cos^2x}{sin^2x}[/tex]
= [tex]\frac{sin^2x}{sin^2x}[/tex] = 1 = right side ⇒ proven
