What is the general solution for arctan(x-1)=0 ?

The general solution for arctan(x-1)=0 is x=1

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arctan(x-1)=0

arctan (x - 1) = 0

x = 1

Solution steps

arctan (x - 1) = 0

Apply trig inverse properties

arctan (x - 1) = 0

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

x - 1 = tan (0)

tan (0) = 0

tan (0)

Use the following trivial identity:

tan (0) = 0

tan (0)

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}

= 0

= 0

x - 1 = 0

x - 1 = 0

Solve

x - 1 = 0 : x = 1

x - 1 = 0

Move

1

to the right side

x - 1 = 0

Add

1

to both sides

x - 1 + 1 = 0 + 1

Simplify

x = 1

x = 1

x = 1

sin (2 x - arctan (1)) = \frac{1}{2}

sin (2 θ) = - \frac{2 6}{7}

(sin (x) - 1) (tan (x) + 2) = 0

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

cos^{2} (x) = \frac{( 6 k - 7 )}{7}

What is the general solution for arctan(x-1)=0 ?
The general solution for arctan(x-1)=0 is x=1