What is the general solution for cot(x)cos^2(x)=2cot(x),0<= x<= 2pi ?

The general solution for cot(x)cos^2(x)=2cot(x),0<= x<= 2pi is x= pi/2 ,x=(3pi)/2

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cot(x)cos^2(x)=2cot(x),0<= x<= 2pi

cot (x) cos^{2} (x) = 2 cot (x), 0 \leq x \leq 2 π

x = \frac{π}{2}, x = \frac{3 π}{2}

Solution steps

cot (x) cos^{2} (x) = 2 cot (x), 0 \leq x \leq 2 π

Subtract

2 cot (x)

from both sides

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

Factor

cos^{2} (x) cot (x) - 2 cot (x) : cot (x) (cos (x) + 2) (cos (x) - 2)

cot (x) (cos (x) + 2) (cos (x) - 2) = 0

Solving each part separately

cot (x) = 0 or cos (x) + 2 = 0 or cos (x) - 2 = 0

cot (x) = 0, 0 \leq x \leq 2 π : x = \frac{π}{2}, x = \frac{3 π}{2}

cos (x) + 2 = 0, 0 \leq x \leq 2 π :

No Solution

cos (x) - 2 = 0, 0 \leq x \leq 2 π :

No Solution

Combine all the solutions

x = \frac{π}{2}, x = \frac{3 π}{2}

2 cot^{2} (3 θ) = 5 csc (3 θ) - 4

1 - cos^{2} (\frac{x}{2}) = cos^{2} (x)

1 = 2 sin (2 θ)

cos (- x) = \frac{3}{2}

sin (x) = 0.61366

What is the general solution for cot(x)cos^2(x)=2cot(x),0<= x<= 2pi ?
The general solution for cot(x)cos^2(x)=2cot(x),0<= x<= 2pi is x= pi/2 ,x=(3pi)/2