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

The general solution for cos(θ)-tan(θ)cos(θ)=0 is θ= pi/4+pin

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cos(θ)-tan(θ)cos(θ)=0

cos (θ) - tan (θ) cos (θ) = 0

θ = \frac{π}{4} + πn

Solution steps

cos (θ) - tan (θ) cos (θ) = 0

Factor

cos (θ) - tan (θ) cos (θ) : - cos (θ) (tan (θ) - 1)

- cos (θ) (tan (θ) - 1) = 0

Solving each part separately

cos (θ) = 0 or tan (θ) - 1 = 0

cos (θ) = 0 : θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

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

Combine all the solutions

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn, θ = \frac{π}{4} + πn

Since the equation is undefined for:

\frac{π}{2} + 2 πn, \frac{3 π}{2} + 2 πn

θ = \frac{π}{4} + πn

tan (x - \frac{π}{2}) + 1 = 0

\frac{sin ( x )}{1 - cos ( x )} = csc (x)

2 sin^{2} (θ) + 13 sin (θ) + 6 = 0

- 3 tan (- x) = 5 tan (x) - 3

tan (a) = 22

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