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

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

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cos(x)=(cot^2(x))/(csc^2(x))

cos (x) = \frac{cot ^{2} ( x )}{csc ^{2} ( x )}

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

Solution steps

cos (x) = \frac{cot ^{2} ( x )}{csc ^{2} ( x )}

Subtract

\frac{cot ^{2} ( x )}{csc ^{2} ( x )}

from both sides

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

Simplify

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

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

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

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

Express with sin, cos

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

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

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

Solve by substitution

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

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

cos (x) = 1 : x = 2 πn

Combine all the solutions

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

Since the equation is undefined for:

2 πn

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

2 tan^{2} (x) - 3 cot^{2} (x) = 5

x, 13 y = cos^{4} (1 - 2 x)

cos (x) + cos^{2} (x) + cos^{3} (x) = 0

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

sin^{2} (x) + cos^{5} (x) = 2

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