Verified answer

Remember that the tangent of π/4 is 1. And, whenever the reference angle is π/4, the tangent will be either 1 or -1. The tangent is positive if the angle is in quadrants I or III.

If 0 ≤ x ≤ π, then (multiplying through by 2) 0 ≤ 2x ≤ 2π.

There are two solutions on the interval from zero to 2π, the quad I solution of π/4 and the quad III solution of 5π/4. This gives

2x = π/4 ==> x = π/8

2x = 5π/4 ==> x = 5π/8.

So the solution set is {π/8, 5π/8}.

***Update****

I didn't read this as the tangent squared; I read it as tangent of 2x.

If the equation is tan²(x) = 1, then there are two equations

tan(x) = 1 or tan(x) = -1.

You still use my original observation that tan(π/4) = 1 and any time the reference angle is π/4, the tangent is either +1 or -1. For the interval from zero to π, there are only two solutions.

The quadrant I solution is x = π/4. The quadrant II solution is x = 3π/4. Note that 3π/4 would have reference angle π/4. So the solution set is

{π/4, 3π/4}.

You need to be more careful about how you write things. tan2 x doesn't look like tangent squared. If you want to write tangent squared, type "tan^2(x)". The carrot symbol "^" indicates a power. Also, you write that the solutions are

3/4π

4/π

Both of these are wrong. They contain the correct symbols, but "4/π" is "four divided by pi". One of the answers is "pi divided by four". It should be typed as "π/4". Its not clear if "3/4π" is meant to say that the π is in the numerator or the denominator.

You'll get better answers if people can understand your questions.

3(tan^2)x + tan x = a million enable y= tan x 3y^2+y-a million = 0 This equation is of form ay^2+via+c =0 a = 3 b = a million c = -a million y=[-b+/-sqrt(b^2-4ac)]/2a] y=[-a million +/-sqrt(a million^2-4(3)(-a million)]/(2)(3) discriminant is b^2-4ac =13 y=[-a million +?(13)] / (2)(3) y=[-a million -?(13)] / (2)(3) y = (-a million+?13) / 6 and (-a million-?13) / 6 tan x = (-a million+?13) / 6 x = arctan [ (-a million+?13) / 6 ] = 0.4097 radians tan x = (-a million-?13) / 6 x = arctan [ (-a million-?13) / 6 ] = -0.6547 radians = 5.6285 radians

2x = arctan(1)

2x = pi/ 4

x = pi/ 8