SOLUTION: Given the equation: (sec x - 1)(sec x + 1) = 3 Solve for x: State which trigonometric identity/ies will give a result of 3. Please include a solution too, thank you so much.

Question 1173760: Given the equation:
(sec x - 1)(sec x + 1) = 3
Solve for x: State which trigonometric identity/ies will give a result of 3. Please include a solution too, thank you so much.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Difference of squares rule

Apply one of the pythagorean trig identities

Apply the square root to both sides

or Break up the plus minus into two separate equations

or Arctangent is the same as inverse tangent.

or Use the unit circle. Note that tan(pi/3) = sqrt(3) and tan(-pi/3) = -sqrt(3). The portion is needed to capture all possible solutions for each arctan equation solved.

----------------------------------------

Answer:

The full solution set consists of x values such that
or
where n is any integer

One example solution is . In this case, we use n = 2 on the first equation shown above.

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