What are all the exact solutions of -3tan^2x+1=0? give your answers in radians.

x = π n_1 + π/6 for n_1 element Z

or x = π n_2 - π/6 for n_2 element Z

Step-by-step explanation:

Solve for x:

1 - 3 tan^2(x) = 0

Subtract 1 from both sides:

-3 tan^2(x) = -1

Divide both sides by -3:

tan^2(x) = 1/3

Take the square root of both sides:

tan(x) = 1/sqrt(3) or tan(x) = -1/sqrt(3)

Take the inverse tangent of both sides:

x = π n_1 + π/6 for n_1 element Z

or tan(x) = -1/sqrt(3)

Take the inverse tangent of both sides:

 x = π n_1 + π/6 for n_1 element Z

or x = π n_2 - π/6 for n_2 element Z

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step-by-step explanation:

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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