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

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

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tan^2(x)cos(x)=tan^2(x)

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

x = πn

Solution steps

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

Subtract

tan^{2} (x)

from both sides

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

Factor

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

tan^{2} (x) (cos (x) - 1) = 0

Solving each part separately

tan^{2} (x) = 0 or cos (x) - 1 = 0

tan^{2} (x) = 0 : x = πn

cos (x) - 1 = 0 : x = 2 πn

Combine all the solutions

x = πn, x = 2 πn

Merge Overlapping Intervals

x = πn

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

tan^{3} (x) - tan (x) = 0

8 sin (θ) - 1 = 0

4 sin (θ) cos (θ) = 1

- 64 sin (8 x) = 0

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