What is the general solution for solvefor y,x+tan(xy)=0 ?

The general solution for solvefor y,x+tan(xy)=0 is y=(arctan(-x))/x+(pin)/x

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solvefor y,x+tan(xy)=0

solve for

y, x + tan (x y) = 0

y = \frac{arctan ( - x )}{x} + \frac{πn}{x}

Solution steps

x + tan (x y) = 0

Move

x

to the right side

x + tan (x y) = 0

Subtract

x

from both sides

x + tan (x y) - x = 0 - x

Simplify

tan (x y) = - x

tan (x y) = - x

Apply trig inverse properties

tan (x y) = - x

General solutions for

tan (x y) = - x

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

x y = arctan (- x) + πn

x y = arctan (- x) + πn

Solve

x y = arctan (- x) + πn : y = \frac{arctan ( - x )}{x} + \frac{πn}{x}; x \neq = 0

x y = arctan (- x) + πn

Divide both sides by

x; x \neq = 0

x y = arctan (- x) + πn

Divide both sides by

x; x \neq = 0

\frac{x y}{x} = \frac{arctan ( - x )}{x} + \frac{πn}{x}; x \neq = 0

Simplify

y = \frac{arctan ( - x )}{x} + \frac{πn}{x}; x \neq = 0

y = \frac{arctan ( - x )}{x} + \frac{πn}{x}; x \neq = 0

y = \frac{arctan ( - x )}{x} + \frac{πn}{x}

- sin (2 θ) = 0

∣ cos (2 x) ∣ = 1

sin^{3} (x) = sin^{3} (x) tan (x)

- 4 sin^{2} (θ) - 7 sin (θ) + 7 = 0

2 cos^{2} (4 x) = 1

What is the general solution for solvefor y,x+tan(xy)=0 ?
The general solution for solvefor y,x+tan(xy)=0 is y=(arctan(-x))/x+(pin)/x