Which expression is equivalent to sec^2xcot^2x
A. sin²x
B. csc²x
C. (1)/(cos^2x)
D. (1/(tan^2x)

Answer:
B
Step-by-step explanation:
Using the identities
sec x = [tex]\frac{1}{cosx}[/tex] , csc x = [tex]\frac{1}{sinx}[/tex] , cot x = [tex]\frac{cosx}{sinx}[/tex] , then
sec²x cot²x
= [tex]\frac{1}{cos^2x}[/tex] × [tex]\frac{cos^2x}{sin^2x}[/tex] ( cancel out cos²x )
= [tex]\frac{1}{sin^2x}[/tex]
= csc²x → B