Find all solutions of the following equation on the interval [0,2pi). Sec^2(x)-2=0

interval-02pi

#1

find all solutions of the following equation on the interval [0,2pi).
Sec^2(x)-2=0

Answer:

Sec^2(x)=2

1/sec^2(x)=1/2
cos^2(x)=1/2
cos(x)=+/- Sq root(2)/2

therefore by examining a unit circle, you get that x= pi/4, 3pi/4, 5pi/4, and 7pi/4, from [0,2pi]