What is the general solution for cos^2(x)=cot(x)sin(x) ?

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

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

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

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

Solution steps

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

Subtract

cot (x) sin (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = 1, cos (x) = 0

cos (x) = 1 : x = 2 πn

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Combine all the solutions

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

Since the equation is undefined for:

2 πn

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

sec^{2} (x) csc (x) - 2 csc (x) = 2 - sec^{2} (x)

2 sin (x) = - 2, 0 \leq x \leq 2 π

csc (a) = 3

csc (a) = 5

1 - \frac{1}{2} cos (2 x - \frac{π}{2}) = 0

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