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

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

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cos(θ)=cot(θ)

cos (θ) = cot (θ)

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

Solution steps

cos (θ) = cot (θ)

Subtract

cot (θ)

from both sides

cos (θ) - cot (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

8 cos (x) + 4 sin (2 x) = 0

sin (x) = - \frac{4}{5}, cos (x) < 0, cos (\frac{x}{2})

1 + sin (x) - 2 sin^{2} (x) = 0

y, z = e^{- x} sin (x + 2 y)

3 sin (θ) - 2 sin^{2} (θ) = 0

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