What is the general solution for tan(x)cos(x)+tan(x)=0 ?

The general solution for tan(x)cos(x)+tan(x)=0 is x=pin

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

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

x = πn

Solution steps

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

Factor

tan (x) cos (x) + tan (x) : tan (x) (cos (x) + 1)

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

Solving each part separately

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

tan (x) = 0 : x = πn

cos (x) + 1 = 0 : x = π + 2 πn

Combine all the solutions

x = πn, x = π + 2 πn

Merge Overlapping Intervals

x = πn

sin (θ) = 508

2 = csc (x) cot (x)

sin^{2} (x) = 5

sin^{2} (x) = a

θ, sin (2 θ) = cos (θ)

What is the general solution for tan(x)cos(x)+tan(x)=0 ?
The general solution for tan(x)cos(x)+tan(x)=0 is x=pin