What is the general solution for tan(θ)=(cos(θ))/(sin(θ)) ?

The general solution for tan(θ)=(cos(θ))/(sin(θ)) is θ= pi/4+pin,θ=(3pi)/4+pin

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tan(θ)=(cos(θ))/(sin(θ))

tan (θ) = \frac{cos ( θ )}{sin ( θ )}

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

Solution steps

tan (θ) = \frac{cos ( θ )}{sin ( θ )}

Subtract

\frac{cos ( θ )}{sin ( θ )}

from both sides

tan (θ) - \frac{cos ( θ )}{sin ( θ )} = 0

Simplify

tan (θ) - \frac{cos ( θ )}{sin ( θ )} : \frac{tan ( θ ) sin ( θ ) - cos ( θ )}{sin ( θ )}

\frac{tan ( θ ) sin ( θ ) - cos ( θ )}{sin ( θ )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

tan (θ) sin (θ) - cos (θ) = 0

Express with sin, cos

\frac{- cos ^{2} ( θ ) + sin ^{2} ( θ )}{cos ( θ )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- cos^{2} (θ) + sin^{2} (θ) = 0

Rewrite using trig identities

- cos (2 θ) = 0

Divide both sides by

- 1

cos (2 θ) = 0

General solutions for

cos (2 θ) = 0

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

Solve

2 θ = \frac{π}{2} + 2 πn : θ = \frac{π}{4} + πn

Solve

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

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

sin (θ) + 2 sin^{2} (θ) = 0

(cot (x) + 1) (sin (x) + 1) = 0

cos^{2} (x) - 2 sin (x) = 0

sin (x) cos (2 x) + cos (x) sin (2 x) = \frac{1}{2}

sin (3 x) - 3 sin (x) = 0

What is the general solution for tan(θ)=(cos(θ))/(sin(θ)) ?
The general solution for tan(θ)=(cos(θ))/(sin(θ)) is θ= pi/4+pin,θ=(3pi)/4+pin