What is the general solution for cot(θ)=cos(θ) ?

The general solution for cot(θ)=cos(θ) is θ= pi/2+2pin,θ=(3pi)/2+2pin

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cot(θ)=cos(θ)

cot (θ) = cos (θ)

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

Solution steps

cot (θ) = cos (θ)

Subtract

cos (θ)

from both sides

cot (θ) - cos (θ) = 0

Express with sin, cos

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

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

cos (θ) - cos (θ) sin (θ) = 0

Factor

cos (θ) - cos (θ) sin (θ) : - cos (θ) (sin (θ) - 1)

- cos (θ) (sin (θ) - 1) = 0

Solving each part separately

cos (θ) = 0 or sin (θ) - 1 = 0

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

sin (θ) - 1 = 0 : θ = \frac{π}{2} + 2 πn

Combine all the solutions

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

3 sin^{2} (θ) - cos (θ) + 1 = 0

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

3 csc^{3} (x) - 4 csc (x) = 0

tan (θ) = \frac{6.06}{- 33.5}

csc (θ) = \frac{13}{2}, sec (θ) = \frac{13}{3}

What is the general solution for cot(θ)=cos(θ) ?
The general solution for cot(θ)=cos(θ) is θ= pi/2+2pin,θ=(3pi)/2+2pin