What is the general solution for (2cos(θ))/(tan(θ))=cot(θ) ?

The general solution for (2cos(θ))/(tan(θ))=cot(θ) is θ= pi/3+2pin,θ=(5pi)/3+2pin

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(2cos(θ))/(tan(θ))=cot(θ)

\frac{2 cos ( θ )}{tan ( θ )} = cot (θ)

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Solution steps

\frac{2 cos ( θ )}{tan ( θ )} = cot (θ)

Subtract

cot (θ)

from both sides

\frac{2 cos ( θ )}{tan ( θ )} - cot (θ) = 0

Simplify

\frac{2 cos ( θ )}{tan ( θ )} - cot (θ) : \frac{2 cos ( θ ) - cot ( θ ) tan ( θ )}{tan ( θ )}

\frac{2 cos ( θ ) - cot ( θ ) tan ( θ )}{tan ( θ )} = 0

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

2 cos (θ) - cot (θ) tan (θ) = 0

Rewrite using trig identities

- 1 + 2 cos (θ) = 0

Move

1

to the right side

2 cos (θ) = 1

Divide both sides by

2

cos (θ) = \frac{1}{2}

General solutions for

cos (θ) = \frac{1}{2}

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

sin^{4} (x) = 0

tan (θ) = \frac{7}{24}

- 22 = - 2 sec (x + 15 0^{\circ})

9 sin (θ) + 11 = 0

(4 sin (2 x) + 4 cos (2 x))^{2} = 16

What is the general solution for (2cos(θ))/(tan(θ))=cot(θ) ?
The general solution for (2cos(θ))/(tan(θ))=cot(θ) is θ= pi/3+2pin,θ=(5pi)/3+2pin