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

The general solution for 2cot(x)+1=-1 is x=(3pi)/4+pin

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2cot(x)+1=-1

2 cot (x) + 1 = - 1

x = \frac{3 π}{4} + πn

Degrees

x = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

2 cot (x) + 1 = - 1

Move

1

to the right side

2 cot (x) + 1 = - 1

Subtract

1

from both sides

2 cot (x) + 1 - 1 = - 1 - 1

Simplify

2 cot (x) = - 2

2 cot (x) = - 2

Divide both sides by

2

2 cot (x) = - 2

Divide both sides by

2

\frac{2 cot ( x )}{2} = \frac{- 2}{2}

Simplify

cot (x) = - 1

cot (x) = - 1

General solutions for

cot (x) = - 1

cot (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

sin (θ) = \frac{3}{5}, cos (θ)

cos (2 θ) + 2 cos^{2} (θ) = 0

csc^{2} (t) = 3

3 sin^{2} (θ) + 3 sin (θ) + 3 = 7 sin (θ) + 7

3 cos (x) = cos (x) - 1

What is the general solution for 2cot(x)+1=-1 ?
The general solution for 2cot(x)+1=-1 is x=(3pi)/4+pin