What is the general solution for cot^2(x)+csc(x)=1,0<= x<2pi ?

The general solution for cot^2(x)+csc(x)=1,0<= x<2pi is x= pi/2 ,x=(7pi)/6 ,x=(11pi)/6

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cot^2(x)+csc(x)=1,0<= x<2pi

cot^{2} (x) + csc (x) = 1, 0 \leq x < 2 π

x = \frac{π}{2}, x = \frac{7 π}{6}, x = \frac{11 π}{6}

Solution steps

cot^{2} (x) + csc (x) = 1, 0 \leq x < 2 π

Subtract

1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

csc (x) = 1, 0 \leq x < 2 π : x = \frac{π}{2}

csc (x) = - 2, 0 \leq x < 2 π : x = \frac{7 π}{6}, x = \frac{11 π}{6}

Combine all the solutions

x = \frac{π}{2}, x = \frac{7 π}{6}, x = \frac{11 π}{6}

81 π = 10.5 - 9 cos (\frac{π}{30} t)

5 - 9 cos (x) = 0

tan^{2} (x) = 500

cot (x) + tan (x) = 1

2 cos (x) - 3 sin (x) = - 2

What is the general solution for cot^2(x)+csc(x)=1,0<= x<2pi ?
The general solution for cot^2(x)+csc(x)=1,0<= x<2pi is x= pi/2 ,x=(7pi)/6 ,x=(11pi)/6