Question

Sec2x= ____. select all that apply

Answer 1

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

Simplifying 1st option:
$\frac{1}{ cos^{2}x - sin^{2}x }= \frac{1}{cos(2x)}=sec(2x)$

Simplifying 2nd option:
$\frac{1}{1- 2sin^{2}x } = \frac{1}{cos(2x)}=sec(2x)$

Simplifying 3rd option:
$\frac{1}{ sin^{2}x - cos^{2}x } = \frac{1}{-cos(2x)} =-sec(2x)$

Simplifying 4th option:
$\frac{1}{2 sin^{2}x }= \frac{ cosec^{2}x }{2}$

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