What is the general solution for arctan(2x-3)= pi/4 ?

The general solution for arctan(2x-3)= pi/4 is x=2

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arctan(2x-3)= pi/4

arctan (2 x - 3) = \frac{π}{4}

x = 2

Solution steps

arctan (2 x - 3) = \frac{π}{4}

Apply trig inverse properties

arctan (2 x - 3) = \frac{π}{4}

arctan (x) = a \Rightarrow x = tan (a)

2 x - 3 = tan (\frac{π}{4})

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

Use the following trivial identity:

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

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}

= 1

= 1

2 x - 3 = 1

2 x - 3 = 1

Solve

2 x - 3 = 1 : x = 2

2 x - 3 = 1

Move

3

to the right side

2 x - 3 = 1

Add

3

to both sides

2 x - 3 + 3 = 1 + 3

Simplify

2 x = 4

2 x = 4

Divide both sides by

2

2 x = 4

Divide both sides by

2

\frac{2 x}{2} = \frac{4}{2}

Simplify

x = 2

x = 2

x = 2

cos (x) = - 0, 5

tan (2 x) + 2 cos (x) = 0, 0 \leq x \leq 2 π

x, cos^{2} (x) = 2 + 2 sin (x)

1 - sin (x) = 1

- sin (2 x) = \frac{cos ( 2 x )}{3}

What is the general solution for arctan(2x-3)= pi/4 ?
The general solution for arctan(2x-3)= pi/4 is x=2