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

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

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

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

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

Solution steps

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

Subtract

1 + csc (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

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

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

Combine all the solutions

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

7 tan (A) + 42 = 0

2 sin (x + \frac{π}{4}) = 1

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

sin (x + \frac{π}{4}) = - \frac{2}{2}, 0 \leq x \leq 2 π

1 + 2 sin^{2} (x) = - 5 cos (x)

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