What is the general solution for sec(x)cot(x)=-2 ?

The general solution for sec(x)cot(x)=-2 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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sec(x)cot(x)=-2

sec (x) cot (x) = - 2

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

Solution steps

sec (x) cot (x) = - 2

Subtract

- 2

from both sides

sec (x) cot (x) + 2 = 0

Express with sin, cos

\frac{1 + 2 sin ( x )}{sin ( x )} = 0

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

1 + 2 sin (x) = 0

Move

1

to the right side

2 sin (x) = - 1

Divide both sides by

2

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

General solutions for

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

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

sin^{2} (x) = \frac{( 4 m - 9 )}{8}

- csc (x) = 1

sin (θ) = - \frac{7}{4}

x, sin (x) = e^{y}

sin^{4} (x) - sin^{2} (x) + 1 = 0

What is the general solution for sec(x)cot(x)=-2 ?
The general solution for sec(x)cot(x)=-2 is x=(7pi)/6+2pin,x=(11pi)/6+2pin