What is the general solution for solvefor x,arctan(x+y)=y^2+pi/4 ?

The general solution for solvefor x,arctan(x+y)=y^2+pi/4 is x=tan(y^2+pi/4)-y

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solvefor x,arctan(x+y)=y^2+pi/4

solve for

x, arctan (x + y) = y^{2} + \frac{π}{4}

x = tan (y^{2} + \frac{π}{4}) - y

Solution steps

arctan (x + y) = y^{2} + \frac{π}{4}

Apply trig inverse properties

arctan (x + y) = y^{2} + \frac{π}{4}

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

x + y = tan (y^{2} + \frac{π}{4})

x + y = tan (y^{2} + \frac{π}{4})

Solve

x + y = tan (y^{2} + \frac{π}{4}) : x = tan (y^{2} + \frac{π}{4}) - y

x + y = tan (y^{2} + \frac{π}{4})

Move

y

to the right side

x + y = tan (y^{2} + \frac{π}{4})

Subtract

y

from both sides

x + y - y = tan (y^{2} + \frac{π}{4}) - y

Simplify

x = tan (y^{2} + \frac{π}{4}) - y

x = tan (y^{2} + \frac{π}{4}) - y

x = tan (y^{2} + \frac{π}{4}) - y

- sin (x) + ln (2) \cdot cos^{2} (x) = 0

cot (x) sec (x) + 2 cot (x) = 0

5 sin (x) - 20 = - 15

cos (x) = \frac{11}{14}

2 sin (θ) cos (θ) + 2 sin (θ) = 0

What is the general solution for solvefor x,arctan(x+y)=y^2+pi/4 ?
The general solution for solvefor x,arctan(x+y)=y^2+pi/4 is x=tan(y^2+pi/4)-y