Find the positive angle, which satisfies the equation tan^2(x) - tan(x) = 0 I know the answer, but I don't quite understand how to do the question. Please explain how you got the answer if you can.

Given the equation:

tan^2(x) - tan (x) = 0

Find the positive angle.

Solution:

Notice that the given equation is factorable by tan(x), therefore we will factor it out to simplify.

tan^2(x) - tan (x) = 0

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

Equate the values to 0 and solve for the angle individually.

tan(x) = 0, and tan(x) - 1 = 0

tan(x) = 0

Tan is equal to zero at O degrees, with point (1,0)

Tan = y/x

Tan = 0/1

Tan(x) = 0, therefore

Tan(x) = 0 degrees

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tan(x) - 1 = 0

tan(x) = 1

tan(x) = 45 degrees and 225 degrees

45 degrees contains the point (√2/2,√2/2), and 225 degrees contains the point (-√2/2,-√2/2), in the trigonometric unit circle.

tan = √2/2 / √2/2 

tan  = 1

tan = -√2/2 / -√2/2

tan = 1

The values cancel out leaving the answer 1.

Tan(x) = 1, therefore

Tan(x) = 45 degrees and 225 degrees