Question

Which expression is equivalent to sec^2xcot^2x

A. sin²x
B. csc²x
C. (1)/(cos^2x)
D. (1/(tan^2x)

Answer 1

B

Explanation:

Using the identities

sec x =
`(1)/(cosx)` , csc x =
`(1)/(sinx)` , cot x =
`(cosx)/(sinx)` , then

sec²x cot²x

=
`(1)/(cos^2x)` ×
`(cos^2x)/(sin^2x)` ( cancel out cos²x )

=
`(1)/(sin^2x)`

= csc²x → B