Question

Sec2x= ____. select all that apply

1/cos^2x-sin^2x
1/1-2sin^2x
1/sin^2x-cos^2x
1/2sin^2x

Answer 1

Answer: the first 2:

1/cos^2x-sin^2x

1/1-2sin^2x

Explanation:

A P E X

Answer 2

The best way to solve such questions is to simplify the options and see what they result in:

Simplifying 1st option:

`(1)/( cos^(2)x - sin^(2)x )= (1)/(cos(2x))=sec(2x)`

Simplifying 2nd option:

`(1)/(1- 2sin^(2)x ) = (1)/(cos(2x))=sec(2x)`

Simplifying 3rd option:

`(1)/( sin^(2)x - cos^(2)x ) = (1)/(-cos(2x)) =-sec(2x)`

Simplifying 4th option:

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

So only first two option are the correct ones as they simplify to sec(2x).