What is the general solution for (cos(x))/(1-cos^2(x))= 2/3 ?

The general solution for (cos(x))/(1-cos^2(x))= 2/3 is x= pi/3+2pin,x=(5pi)/3+2pin

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(cos(x))/(1-cos^2(x))= 2/3

\frac{cos ( x )}{1 - cos ^{2} ( x )} = \frac{2}{3}

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

Solution steps

\frac{cos ( x )}{1 - cos ^{2} ( x )} = \frac{2}{3}

Solve by substitution

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

cos (x) = - 2 :

No Solution

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

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

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

- sec^{2} (x) - 5 = 2 sec (x) - 4

2 sin^{2} (x) + 2 sin (x) = 0

8 sin (x) cos (x) = 0

cos (θ) = \frac{9}{41}

What is the general solution for (cos(x))/(1-cos^2(x))= 2/3 ?
The general solution for (cos(x))/(1-cos^2(x))= 2/3 is x= pi/3+2pin,x=(5pi)/3+2pin