Question

Find all solutions in the interval [0, 2π). sec2 x - 2 = tan2 x PLZ HELP!!!

Answer 1

The equation is equivalent to 1/cos(2x)-2=sin(2x)/cos(2x).
 Make the denominator cos(2x) for all terms, we get
 1-2cos(2x)=sin(2x).
 Since cos^2(2x)+sin^2(2x)=1,
 let cos(2x)=a,
 substitute sin(2x) by
 +-\sqrt(1-a^2),
 and solve the equation with only one variable a.
 We get a=4/5 or 0,
 but cos(2x) cannot be 0,
 otherwise sec(2x) is undefined.
 2x=36.9 degrees,
 so x=18.9 degrees 
 in radians we have 
 x=(18.9/180)*pi=0.33
 answer 
 0.33 (it is between [0, 2π))