Solve the equation sec^2(x) - 4tan(x)= -3 , 0 ≤x≤ 2π

To solve this problem, we have to look at some trig. identities that will help us simplify the problem.The formula booklet is always a great place to start! You can find that sec^2(x) = 1 + tan^2(x). Substituting this into the equation yields tan^2(x) + 1 - 4tan(x) = -3 Move the three over, and you will have tan^2(x) - 4tan(x) + 4 = 0 From here, you can factorize to [ tan(x) - 2 ] ^2 = 0, which gives you tan x = 2arctan(2) = 1.01 radians (63.4 degrees), 4.25 radians (243.4 degrees)
One common point that catches people out is they forget to put two solutions instead of one. Remember, that for any trigonometric function, it will repeat itself in a cyclical manner. Think of the graph, and even sketch it out to get a rough idea of where your solutions will fall, so that you can reach the answer more quickly and accurately