What is the general solution for tan(2x+3)=1 ?

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

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tan(2x+3)=1

tan (2 x + 3) = 1

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

Degrees

x = - 63.44366 \dots^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 x + 3) = 1

General solutions for

tan (2 x + 3) = 1

tan (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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{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

Subtract

3

from 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}

6 cos^{2} (x) - 5 cos (x) + 1 = 0

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

tan (\frac{x}{2}) = \frac{1}{3}

6 cos (x) = 5

6 cos (2 x) = 6 cos^{2} (x) - 5

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