What is the general solution for tan(x-pi/4)= 1/6 ?

The general solution for tan(x-pi/4)= 1/6 is x=0.16514…+pin+pi/4

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tan(x-pi/4)= 1/6

tan (x - \frac{π}{4}) = \frac{1}{6}

x = 0.16514 \dots + πn + \frac{π}{4}

Degrees

x = 54.46232 \dots^{\circ} + 18 0^{\circ} n

Solution steps

tan (x - \frac{π}{4}) = \frac{1}{6}

Apply trig inverse properties

tan (x - \frac{π}{4}) = \frac{1}{6}

General solutions for

tan (x - \frac{π}{4}) = \frac{1}{6}

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

x - \frac{π}{4} = arctan (\frac{1}{6}) + πn

x - \frac{π}{4} = arctan (\frac{1}{6}) + πn

Solve

x - \frac{π}{4} = arctan (\frac{1}{6}) + πn : x = arctan (\frac{1}{6}) + πn + \frac{π}{4}

x - \frac{π}{4} = arctan (\frac{1}{6}) + πn

Move

\frac{π}{4}

to the right side

x - \frac{π}{4} = arctan (\frac{1}{6}) + πn

Add

\frac{π}{4}

to both sides

x - \frac{π}{4} + \frac{π}{4} = arctan (\frac{1}{6}) + πn + \frac{π}{4}

Simplify

x = arctan (\frac{1}{6}) + πn + \frac{π}{4}

x = arctan (\frac{1}{6}) + πn + \frac{π}{4}

x = arctan (\frac{1}{6}) + πn + \frac{π}{4}

Show solutions in decimal form

x = 0.16514 \dots + πn + \frac{π}{4}

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

arccos (\frac{3}{2}) + arcsin (3 x) = \frac{π}{2}

2 sin (x) = 5 cos (x), 0^{\circ} \leq x < 36 0^{\circ}

cos (x) = \frac{1 - 2}{26}

4 cos (2 x) - 2 sin (2 x) = 0

What is the general solution for tan(x-pi/4)= 1/6 ?
The general solution for tan(x-pi/4)= 1/6 is x=0.16514…+pin+pi/4