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

The general solution for sqrt(2)tan(x)cos(x)=tan(x) is x=pin,x= pi/4+2pin,x=(7pi)/4+2pin

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sqrt(2)tan(x)cos(x)=tan(x)

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

x = πn, x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Solution steps

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

Subtract

tan (x)

from both sides

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

Factor

2 tan (x) cos (x) - tan (x) : tan (x) (2 cos (x) - 1)

tan (x) (2 cos (x) - 1) = 0

Solving each part separately

tan (x) = 0 or 2 cos (x) - 1 = 0

tan (x) = 0 : x = πn

2 cos (x) - 1 = 0 : x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Combine all the solutions

x = πn, x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

sin (x) = \frac{5}{4}

sin (2 θ) = 3 cos (θ)

x, tan (x) + ∣ tan (x) ∣ = 1

0 = 2 sin^{2} (θ) + 3 sin (θ)

y, x = arctan (x + y)

What is the general solution for sqrt(2)tan(x)cos(x)=tan(x) ?
The general solution for sqrt(2)tan(x)cos(x)=tan(x) is x=pin,x= pi/4+2pin,x=(7pi)/4+2pin