How would you find this constant K

In determining the path of a radiated particle moving through a charged field it is necessary to determine a constant, which equals the expression:

2sec^2X – 2sec^2Xsin^2X – sin^2X – cos^2X. Find this constant K.

What does this problem even mean?

Simplify the trig expression using known identities to get a value
as in....

2sec^2(x) - 2sec^2(x)sin^2(x) - sin^2(x) -cos^2(x)
= 2sec^2(x)(1 - sin^2(x)) - (sin^2(x) + cos^2(x))
= 2sec^2(x)cos^2(x) - 1
= 2 - 1
= 1

You just need to simplify the expression a bit:

2*sec^2(x) - 2*sec^2(x)*sin^2(x) - sin^2(x) - cos^2(x)

= 2*sec^2(x)(1 - sin^2(x)) - (sin^2(x) + cos^2(x))

= 2*sec^2(x)*cos^2(x) - 1

= 2 - 1 = 1