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
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