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

The general solution for tan(x)*cos^2(x)-tan(x)=0 is x=pin

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

tan (x) \cdot cos^{2} (x) - tan (x) = 0

x = πn

Solution steps

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

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 : x = πn

cos (x) + 1 = 0 : x = π + 2 πn

cos (x) - 1 = 0 : x = 2 πn

Combine all the solutions

x = πn, x = π + 2 πn, x = 2 πn

Merge Overlapping Intervals

x = πn

sin (x + π) - sin (x) + 2 = 0

3 tan (x) = - 3

2 (sin (x))^{2} - 5 cos (x) + 1 = 0

5 sin (x) cos (x) = 3 cos (x)

3 cos (x) + sin (x) = 2

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