What is the general solution for 4cot(x)+3=-1 ?

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

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4cot(x)+3=-1

4 cot (x) + 3 = - 1

x = \frac{3 π}{4} + πn

Degrees

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

Solution steps

4 cot (x) + 3 = - 1

Move

3

to the right side

4 cot (x) + 3 = - 1

Subtract

3

from both sides

4 cot (x) + 3 - 3 = - 1 - 3

Simplify

4 cot (x) = - 4

4 cot (x) = - 4

Divide both sides by

4

4 cot (x) = - 4

Divide both sides by

4

\frac{4 cot ( x )}{4} = \frac{- 4}{4}

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

cos (\frac{θ}{2}) - cos (θ) = 1

cot (θ) = \frac{4}{3}

0 = sin (x) - cos (x)

1 - tan^{2} (x) = sec^{2} (x)

cos (2 θ - \frac{π}{2}) = - 1, 0 \leq θ < 2 π

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