Question 1043019
tan^2(x)-1=0


(tan(x)+1)(tan(x)-1)=0 ... difference of squares rule


tan(x)+1=0 or tan(x)-1=0


Let's focus on each sub-equation one at a time. 


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Let's solve the first sub-equation for x.


tan(x)+1=0


tan(x) = -1


x = arctan(-1)


x = 3pi/4 or x = 7pi/4


Note: use the <a href = "https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/2000px-Unit_circle_angles_color.svg.png">unit circle</a> to determine the two angles. Look at where the x and y coordinates are equal and opposite in sign (Quadrant 2 and 4)


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Now move onto the next


tan(x)-1 = 0


tan(x) = 1


x = arctan(1)


x = pi/4 or x = 5pi/4


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The four solutions are:
x = pi/4
x = 3pi/4
x = 5pi/4
x = 7pi/4