I am trying to solve a problem from a study manual for the NYSTCE. I think the manual might be breaking some mathematical laws. Someone please throw a life raft.
The problem is as follows:
What is the sum, in radians, of the solutions for x in the following equation?
Tan2x = (3/2)(sec x)
The manual gives a detailed explanation:
It rewrites Tan2x as sec2x-1 to arrive at the equation below.
sec2x-1 = (3/2) (sec x)
The manual loses me when it writes the equation above then as:
2sec2x - 3secx - 2 = 0
How is this so? I am lost on this step. Maybe I am missing a rule. Help on this problem would be greatly appreciated.