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

Which expression is equivalent to sec2xcot2x A sinx B cscx C 1cos2x D 1tan2x class=

Respuesta :

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