What is the general solution for solvefor x,e^y=tan(x+pi/3) ?

The general solution for solvefor x,e^y=tan(x+pi/3) is x=arctan(e^y)+pin-pi/3

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solvefor x,e^y=tan(x+pi/3)

solve for

x, e^{y} = tan (x + \frac{π}{3})

x = arctan (e^{y}) + πn - \frac{π}{3}

Solution steps

e^{y} = tan (x + \frac{π}{3})

Switch sides

tan (x + \frac{π}{3}) = e^{y}

Apply trig inverse properties

tan (x + \frac{π}{3}) = e^{y}

General solutions for

tan (x + \frac{π}{3}) = e^{y}

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

x + \frac{π}{3} = arctan (e^{y}) + πn

x + \frac{π}{3} = arctan (e^{y}) + πn

Solve

x + \frac{π}{3} = arctan (e^{y}) + πn : x = arctan (e^{y}) + πn - \frac{π}{3}

x + \frac{π}{3} = arctan (e^{y}) + πn

Move

\frac{π}{3}

to the right side

x + \frac{π}{3} = arctan (e^{y}) + πn

Subtract

\frac{π}{3}

from both sides

x + \frac{π}{3} - \frac{π}{3} = arctan (e^{y}) + πn - \frac{π}{3}

Simplify

x = arctan (e^{y}) + πn - \frac{π}{3}

x = arctan (e^{y}) + πn - \frac{π}{3}

x = arctan (e^{y}) + πn - \frac{π}{3}

cos (x) = (sin (x))^{2} - 1

3 cos^{2} (x) - sin (x) - 1 = 0

tan^{2} (θ) sin (θ) = tan^{2} (θ)

cos (x) = \frac{1}{cot ( x )}

(sin (x) - 1) \cdot (sin (x) - 3) = 0

What is the general solution for solvefor x,e^y=tan(x+pi/3) ?
The general solution for solvefor x,e^y=tan(x+pi/3) is x=arctan(e^y)+pin-pi/3