What is the general solution for cot(2x-3)-1=0 ?

The general solution for cot(2x-3)-1=0 is x= 3/2+pi/8+(pin)/2

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cot(2x-3)-1=0

Solution

cot (2 x - 3) - 1 = 0

Solution

x = \frac{3}{2} + \frac{π}{8} + \frac{πn}{2}

Degrees

x = 108.44366 \dots^{\circ} + 9 0^{\circ} n

Solution steps

cot (2 x - 3) - 1 = 0

Move

1

to the right side

cot (2 x - 3) - 1 = 0

Add

1

to both sides

cot (2 x - 3) - 1 + 1 = 0 + 1

Simplify

cot (2 x - 3) = 1

cot (2 x - 3) = 1

General solutions for

cot (2 x - 3) = 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

2 x - 3 = \frac{π}{4} + πn

2 x - 3 = \frac{π}{4} + πn

Solve

2 x - 3 = \frac{π}{4} + πn : x = \frac{3}{2} + \frac{π}{8} + \frac{πn}{2}

2 x - 3 = \frac{π}{4} + πn

Move

3

to the right side

2 x - 3 = \frac{π}{4} + πn

Add

3

to both sides

2 x - 3 + 3 = \frac{π}{4} + πn + 3

Simplify

2 x = \frac{π}{4} + πn + 3

2 x = \frac{π}{4} + πn + 3

Divide both sides by

2

2 x = \frac{π}{4} + πn + 3

Divide both sides by

2

\frac{2 x}{2} = \frac{\frac{π}{4}}{2} + \frac{πn}{2} + \frac{3}{2}

Simplify

\frac{2 x}{2} = \frac{\frac{π}{4}}{2} + \frac{πn}{2} + \frac{3}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{π}{4}}{2} + \frac{πn}{2} + \frac{3}{2} : \frac{3}{2} + \frac{π}{8} + \frac{πn}{2}

\frac{\frac{π}{4}}{2} + \frac{πn}{2} + \frac{3}{2}

Group like terms

= \frac{3}{2} + \frac{πn}{2} + \frac{\frac{π}{4}}{2}

\frac{\frac{π}{4}}{2} = \frac{π}{8}

\frac{\frac{π}{4}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

= \frac{π}{8}

= \frac{3}{2} + \frac{πn}{2} + \frac{π}{8}

Group like terms

= \frac{3}{2} + \frac{π}{8} + \frac{πn}{2}

x = \frac{3}{2} + \frac{π}{8} + \frac{πn}{2}

x = \frac{3}{2} + \frac{π}{8} + \frac{πn}{2}

x = \frac{3}{2} + \frac{π}{8} + \frac{πn}{2}

x = \frac{3}{2} + \frac{π}{8} + \frac{πn}{2}

Popular Examples

4sin^{32}(x)-3cos^2(x)=0

4 sin^{32} (x) - 3 cos^{2} (x) = 0

4tan^2(x)+15sec(x)=0

4 tan^{2} (x) + 15 sec (x) = 0

sin^4(x)+cos^4(x)=cos^4(x)

sin^{4} (x) + cos^{4} (x) = cos^{4} (x)

cot(x)= 40/32

cot (x) = \frac{40}{32}

tan(a)= 3/8

tan (a) = \frac{3}{8}

Frequently Asked Questions (FAQ)

What is the general solution for cot(2x-3)-1=0 ?
The general solution for cot(2x-3)-1=0 is x= 3/2+pi/8+(pin)/2