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Popular >

cot(x)sin^2(x)=4cot(x)

Solution

cot (x) sin^{2} (x) = 4 cot (x)

Solution

x = \frac{π}{2} + πn

+1

Solution steps

cot (x) sin^{2} (x) = 4 cot (x)

Subtract

4 cot (x)

from both sides

sin^{2} (x) cot (x) - 4 cot (x) = 0

Factor

sin^{2} (x) cot (x) - 4 cot (x) : cot (x) (sin (x) + 2) (sin (x) - 2)

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

Solving each part separately

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

cot (x) = 0 : x = \frac{π}{2} + πn

sin (x) + 2 = 0 :

No Solution

sin (x) - 2 = 0 :

No Solution

Combine all the solutions

x = \frac{π}{2} + πn

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x, z = arctan (\frac{x}{y})

- \frac{1}{2} = cos (θ)

4cos^2(x)-3cos(x)-2=0

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

sin (x) = cos (3 x)

Frequently Asked Questions (FAQ)

What is the general solution for cot(x)sin^2(x)=4cot(x) ?
The general solution for cot(x)sin^2(x)=4cot(x) is x= pi/2+pin