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

The general solution for cot^2(a)=cos^2(a)(cot(a)cos(a))^2 is a= pi/2+pin

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cot^2(a)=cos^2(a)(cot(a)cos(a))^2

cot^{2} (a) = cos^{2} (a) (cot (a) cos (a))^{2}

a = \frac{π}{2} + πn

Solution steps

cot^{2} (a) = cos^{2} (a) (cot (a) cos (a))^{2}

Subtract

cos^{2} (a) (cot (a) cos (a))^{2}

from both sides

cot^{2} (a) - cos^{4} (a) cot^{2} (a) = 0

Factor

cot^{2} (a) - cos^{4} (a) cot^{2} (a) : - cot^{2} (a) (cos^{2} (a) + 1) (cos (a) + 1) (cos (a) - 1)

- cot^{2} (a) (cos^{2} (a) + 1) (cos (a) + 1) (cos (a) - 1) = 0

Solving each part separately

cot^{2} (a) = 0 or cos^{2} (a) + 1 = 0 or cos (a) + 1 = 0 or cos (a) - 1 = 0

cot^{2} (a) = 0 : a = \frac{π}{2} + πn

cos^{2} (a) + 1 = 0 :

No Solution

cos (a) + 1 = 0 : a = π + 2 πn

cos (a) - 1 = 0 : a = 2 πn

Combine all the solutions

a = \frac{π}{2} + πn, a = π + 2 πn, a = 2 πn

Since the equation is undefined for:

π + 2 πn, 2 πn

a = \frac{π}{2} + πn

1 + cot^{2} (x) = 8 sin (x)

4 sin^{2} (x) = 8 sin^{2} (\frac{x}{2})

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

cos (\frac{π}{2} - x) = 0

1 sin (4 5^{\circ}) = 2.42 sin (r)

What is the general solution for cot^2(a)=cos^2(a)(cot(a)cos(a))^2 ?
The general solution for cot^2(a)=cos^2(a)(cot(a)cos(a))^2 is a= pi/2+pin