What is the general solution for (1+cos(x))(tan(x)-1)=0 ?

The general solution for (1+cos(x))(tan(x)-1)=0 is x=pi+2pin,x= pi/4+pin

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

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

x = π + 2 πn, x = \frac{π}{4} + πn

Solution steps

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

Solving each part separately

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

1 + cos (x) = 0 : x = π + 2 πn

tan (x) - 1 = 0 : x = \frac{π}{4} + πn

Combine all the solutions

x = π + 2 πn, x = \frac{π}{4} + πn

cos (x) = \pm \frac{1}{2}

\frac{cos ( θ )}{1 + sin ( θ )} = tan (\frac{π}{4} - θ)

sin (x) = \frac{1}{4 sin ( x )}

cos (4 θ) = cos (3 θ)

\frac{- 2 3}{3} = sec (θ)

What is the general solution for (1+cos(x))(tan(x)-1)=0 ?
The general solution for (1+cos(x))(tan(x)-1)=0 is x=pi+2pin,x= pi/4+pin