What is the general solution for 1+csc(x)=cot^2(x) ?

The general solution for 1+csc(x)=cot^2(x) is x=(3pi)/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin

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1+csc(x)=cot^2(x)

1 + csc (x) = cot^{2} (x)

x = \frac{3 π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

1 + csc (x) = cot^{2} (x)

Subtract

cot^{2} (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

csc (x) = - 1, csc (x) = 2

csc (x) = - 1 : x = \frac{3 π}{2} + 2 πn

csc (x) = 2 : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{3 π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

cos (\frac{1}{4 θ}) = \frac{- 2}{2}

cos (x) tan (x) - 2 cos^{2} (x) = - 1

3 cot (\frac{1}{4} x) = 1

2 sin (\frac{π}{4} - x) + 3 = 0

3.1 = 48.1 (1 - cos (\frac{28.66 x}{48.1}))

What is the general solution for 1+csc(x)=cot^2(x) ?
The general solution for 1+csc(x)=cot^2(x) is x=(3pi)/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin