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

The general solution for tan(x)-2tan(x)cos(x)=0 is x=pin,x= pi/3+2pin,x=(5pi)/3+2pin

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

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

x = πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

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

Factor

tan (x) - 2 tan (x) cos (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}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sin (t) cos (t) = cos (t)

- 7 cos (7 x) = 0

1 - 4 sin^{2} (x) = 0

cos (2 θ) - 6 sin^{2} (θ) = - 5

sin (A) = \frac{15}{17}

What is the general solution for tan(x)-2tan(x)cos(x)=0 ?
The general solution for tan(x)-2tan(x)cos(x)=0 is x=pin,x= pi/3+2pin,x=(5pi)/3+2pin