Solve sec(x)^2-2*tan(x)=4 for 0<=x<=360
We know sin(x)^2+cos(x)^2=1Dividing by cos(x)^2: tan(x)^2+1=sec(x)^2Substitute into the Equation and Rearrange to get: tan(x)^2-2*tan(x)-3=0Let y = tan(x): y^2-2y-3=0Factorising: (y-3)(y+1)=0so y = 3 and y = -1 are solutionsCase 1 (y=3):tan(x) = 3Using Calculator: x = 71.565... and since tan repeats every 180 degrees, 251.565... is also a solutionCase 2 (y=-1):tan(x) = -1Using Calculator: x = -45, but this is outside of the region so using the 180 rule twice, we get two more solutions at x = 135 and 315Thus we have 4 solutions
MR
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