What is the general solution for cot(y)+2=1-csc(y) ?

The general solution for cot(y)+2=1-csc(y) is y=2pin+(3pi)/2

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cot(y)+2=1-csc(y)

cot (y) + 2 = 1 - csc (y)

y = 2 πn + \frac{3 π}{2}

Solution steps

cot (y) + 2 = 1 - csc (y)

Subtract

1 - csc (y)

from both sides

cot (y) + csc (y) + 1 = 0

Express with sin, cos

\frac{1 + cos ( y ) + sin ( y )}{sin ( y )} = 0

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

1 + cos (y) + sin (y) = 0

Rewrite using trig identities

1 + 2 sin (y + \frac{π}{4}) = 0

Move

1

to the right side

2 sin (y + \frac{π}{4}) = - 1

Divide both sides by

2

sin (y + \frac{π}{4}) = - \frac{2}{2}

General solutions for

sin (y + \frac{π}{4}) = - \frac{2}{2}

y + \frac{π}{4} = \frac{5 π}{4} + 2 πn, y + \frac{π}{4} = \frac{7 π}{4} + 2 πn

Solve

y + \frac{π}{4} = \frac{5 π}{4} + 2 πn : y = 2 πn + π

Solve

y + \frac{π}{4} = \frac{7 π}{4} + 2 πn : y = 2 πn + \frac{3 π}{2}

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

Since the equation is undefined for:

2 πn + π

y = 2 πn + \frac{3 π}{2}

2 sin (x) + cos (x) = - 1

sec^{2} (x) + 7 tan (x) = 9

1 - 3 cos (θ) = sin^{2} (θ)

cot (2 x) = - 1

cos^{3} (x) - sin^{3} (x) = 0

What is the general solution for cot(y)+2=1-csc(y) ?
The general solution for cot(y)+2=1-csc(y) is y=2pin+(3pi)/2