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

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

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sin(θ)cos(θ)=cot(θ)

sin (θ) cos (θ) = cot (θ)

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

Solution steps

sin (θ) cos (θ) = cot (θ)

Subtract

cot (θ)

from both sides

sin (θ) cos (θ) - cot (θ) = 0

Express with sin, cos

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

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

- cos (θ) + cos (θ) sin^{2} (θ) = 0

Factor

- cos (θ) + cos (θ) sin^{2} (θ) : cos (θ) (sin (θ) + 1) (sin (θ) - 1)

cos (θ) (sin (θ) + 1) (sin (θ) - 1) = 0

Solving each part separately

cos (θ) = 0 or sin (θ) + 1 = 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{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

cot (θ) = - \frac{4}{3}

tan (x) = \frac{6}{10}

tan (A) = 34

2 sec (x) = 2

- 2 cos (2 θ) + 9 cos (θ) + 4 = cos (θ) + 1

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