What is the general solution for 4cot(θ)sin(θ)=2 ?

The general solution for 4cot(θ)sin(θ)=2 is θ= pi/3+2pin,θ=(5pi)/3+2pin

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4cot(θ)sin(θ)=2

4 cot (θ) sin (θ) = 2

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

Solution steps

4 cot (θ) sin (θ) = 2

Subtract

2

from both sides

4 cot (θ) sin (θ) - 2 = 0

Rewrite using trig identities

- 2 + 4 cos (θ) = 0

Move

2

to the right side

4 cos (θ) = 2

Divide both sides by

4

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

2 sin (2 x) - 5 tan (2 x) = 0

75 = \frac{120}{4} \cdot cos (\frac{2 \cdot π \cdot x}{360}) + \frac{120}{2}

cot^{2} (x) + 2 = 2 csc (x)

3 sin (x) + cos (x) = 2

15 cos^{2} (x) - 4 cos (x) - 3 = 0

What is the general solution for 4cot(θ)sin(θ)=2 ?
The general solution for 4cot(θ)sin(θ)=2 is θ= pi/3+2pin,θ=(5pi)/3+2pin