What is the general solution for tan(x)cos^2(x)-tan(x)=0,(0,2pi) ?

The general solution for tan(x)cos^2(x)-tan(x)=0,(0,2pi) is x=pi

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tan(x)cos^2(x)-tan(x)=0,(0,2pi)

tan (x) cos^{2} (x) - tan (x) = 0, (0, 2 π)

x = π

Solution steps

tan (x) cos^{2} (x) - tan (x) = 0, (0, 2 π)

Factor

tan (x) cos^{2} (x) - tan (x) : tan (x) (cos (x) + 1) (cos (x) - 1)

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

Solving each part separately

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

tan (x) = 0, (0, 2 π) : x = π

cos (x) + 1 = 0, (0, 2 π) : x = π

cos (x) - 1 = 0, (0, 2 π) :

No Solution

Combine all the solutions

x = π

cos (A) - 1 = 0

4 sin (x) + 7 = 3

1 - cos (4 x) = sin (2 x)

tan (θ) = \frac{2}{1}

cos (2 x) = sin^{2} (x)

What is the general solution for tan(x)cos^2(x)-tan(x)=0,(0,2pi) ?
The general solution for tan(x)cos^2(x)-tan(x)=0,(0,2pi) is x=pi