What is the general solution for solvefor x,tan(x+y+pi/4)=e^y ?

The general solution for solvefor x,tan(x+y+pi/4)=e^y is x=arctan(e^y)+pin-y-pi/4

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solvefor x,tan(x+y+pi/4)=e^y

solve for

x, tan (x + y + \frac{π}{4}) = e^{y}

x = arctan (e^{y}) + πn - y - \frac{π}{4}

Solution steps

tan (x + y + \frac{π}{4}) = e^{y}

Apply trig inverse properties

x + y + \frac{π}{4} = arctan (e^{y}) + πn

Solve

x + y + \frac{π}{4} = arctan (e^{y}) + πn : x = arctan (e^{y}) + πn - y - \frac{π}{4}

x = arctan (e^{y}) + πn - y - \frac{π}{4}

tan (2 x) = 0.75

3 tan^{2} (x) + 7 tan (x) + 4 = 0

cos (2 θ) - 3 = - 5 sin (θ)

sin (2 x) = 0

7 sin^{2} (x) + 3 cos^{2} (x) = 5

What is the general solution for solvefor x,tan(x+y+pi/4)=e^y ?
The general solution for solvefor x,tan(x+y+pi/4)=e^y is x=arctan(e^y)+pin-y-pi/4