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

The general solution for sqrt(2)tan(x)cos(x)-tan(x)=0 is x=pin,x= pi/4+2pin,x=(7pi)/4+2pin

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

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

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

Solution steps

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 (\frac{x}{2}) = 2 - sin (\frac{x}{2})

tan (3 x) = \frac{3}{3}

sin (x) tan (x) = sin (x)

2 cos^{2} (x) + cos (2 x) = 0

9 cos^{2} (θ) - 4 = 0

What is the general solution for sqrt(2)tan(x)cos(x)-tan(x)=0 ?
The general solution for sqrt(2)tan(x)cos(x)-tan(x)=0 is x=pin,x= pi/4+2pin,x=(7pi)/4+2pin