Find all real solutions to four decimal places to the equation sec^2(x)+ 3 tan(x)=5

Answer 1

recall that sec^2 = 1+tan^2, so we have

tan^2(x) + 3tan(x) - 4 = 0
(tan(x)+4)(tan(x)-1) = 0
tan(x) = 1 or -4

So, there will be 4 solutions, one in each quadrant.

Answer 2

don't you just love Wolfram

http://www.wolframalpha.com/input/?i=plot+sec%5E2%28x%29%2B+3+tan%28x%29%3D5%2C+-2π+%3C+x+%3C+2π