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

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

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

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

x = \frac{π}{4} + πn, x = π + 2 πn

Solution steps

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

Solving each part separately

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

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

cos (x) + 1 = 0 : x = π + 2 πn

Combine all the solutions

x = \frac{π}{4} + πn, x = π + 2 πn

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

cos (2 x - \frac{π}{6}) = \frac{3}{2}

12 cos^{2} (θ) = 9

sin (\frac{x}{2}) - 1 = 0

sec (\frac{3 x}{2}) = - 2

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