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

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

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

\frac{cos ( x )}{sin ( x )} = cos^{2} (x)

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

Solution steps

\frac{cos ( x )}{sin ( x )} = cos^{2} (x)

Subtract

cos^{2} (x)

from both sides

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

Simplify

\frac{cos ( x )}{sin ( x )} - cos^{2} (x) : \frac{cos ( x ) - cos ^{2} ( x ) sin ( x )}{sin ( x )}

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

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

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

Factor

cos (x) - cos^{2} (x) sin (x) : cos (x) (1 - sin (x) cos (x))

cos (x) (1 - sin (x) cos (x)) = 0

Solving each part separately

cos (x) = 0 or 1 - sin (x) cos (x) = 0

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

1 - sin (x) cos (x) = 0 :

No Solution

Combine all the solutions

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

sin (2 x - \frac{π}{4}) = 0

7 sin^{2} (θ) - 4 sin (θ) = 3

tan (θ) - cot (θ) = 0

csc^{3} (x) + csc^{2} (x) = \frac{4}{3} csc (x) + \frac{4}{3}

6 sec^{2} (x) tan (x) = 12 tan (x)

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