Solve for x:
(sec(x) - tan(x))^2 = 0

Take the square root of both sides:
sec(x) - tan(x) = 0

Factor sec(x) from the left hand side:
sec(x) (1 - sin(x)) = 0

Multiply both sides by cos(x) assuming cos(x)!=0:
1 - sin(x) = 0 for cos(x)!=0

Subtract 1 from both sides:
-sin(x) = -1 for cos(x)!=0

Multiply both sides by -1:
sin(x) = 1 for cos(x)!=0

Take the inverse sine of both sides:
x = π/2 + 2 π n for cos(x)!=0 and n element Z

The roots x = π/2 + 2 n π violate cos(x)!=0 for all n element Z:
Answer: |False
                   

If you meant "what is the expanded form", then we have:

 

Expand the following:
(tan(x) - sec(x))^2

(tan(x) - sec(x)) (tan(x) - sec(x)) = (tan(x)) (tan(x)) + (tan(x)) (-sec(x)) + (-sec(x)) (tan(x)) + (-sec(x)) (-sec(x)):
tan(x) tan(x) - tan(x) sec(x) - sec(x) tan(x) - ( - sec(x) sec(x))

(-1)^2 = 1:
tan(x) tan(x) - tan(x) sec(x) - sec(x) tan(x) + sec(x) sec(x)

tan(x) tan(x) = tan(x)^2:
tan(x)^2 - tan(x) sec(x) - sec(x) tan(x) + sec(x) sec(x)

sec(x) sec(x) = sec(x)^2:
Answer: |tan(x)^2 - tan(x) sec(x) - sec(x) tan(x) + sec(x)^2