Question

Which expression is equivalent to sec2xcot2x?

A.
sin2x

B.
csc2x

C.
`(1)/(cos^2x)`

D.
`(1)/(tan^2x)`

Answer 1

Yes! The correct answer is option B

Explanation:

B. csc^2x

Answer 2

B. csc²(x)

Explanation:

You can use the relations ...

sec(x) = 1/cos(x)

csc(x) = 1/sin(x)

cot(x) = cos(x)/sin(x)

to replace the functions in your expression. Then you have ...

sec²(x)·cot²(x) = (1/cos(x)·cos(x)/sin(x))² = (1/sin(x))² = csc²(x)

___

Alternate solution

You can also use the relation

cot(x) = csc(x)/sec(x)

Then ...

(sec(x)·cot(x))² = (sec(x)·csc(x)/sec(x))² = csc²(x)