Originally Posted by

**polcareb192** 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?

Tan^{2}x = (3/2)(sec x)

The manual gives a detailed explanation:

It rewrites Tan^{2}x as sec^{2}x-1 to arrive at the equation below.

sec^{2}x-1 = (3/2) (sec x)

The manual loses me when it writes the equation above then as:

2sec^{2}x - 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.