What is the general solution for solvefor x,sin(y/x)+cos(x/y)=0 ?

The general solution for solvefor x,sin(y/x)+cos(x/y)=0 is

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solvefor x,sin(y/x)+cos(x/y)=0

solve for

x, sin (\frac{y}{x}) + cos (\frac{x}{y}) = 0

x = - \frac{- π y - 4 πn y + ( π y + 4 πn y ) ^{2} + 16 y ^{2}}{4}, x = - \frac{- π y - 4 πn y - ( π y + 4 πn y ) ^{2} + 16 y ^{2}}{4}, x = \frac{- π y - 4 πn y + ( π y + 4 πn y ) ^{2} - 16 y ^{2}}{4}, x = \frac{- π y - 4 πn y - ( π y + 4 πn y ) ^{2} - 16 y ^{2}}{4}

Solution steps

sin (\frac{y}{x}) + cos (\frac{x}{y}) = 0

Subtract

sin (\frac{y}{x})

from both sides

cos (\frac{x}{y}) = - sin (\frac{y}{x})

Rewrite using trig identities

sin (\frac{π}{2} - \frac{x}{y}) = sin (- \frac{y}{x})

Apply trig inverse properties

- \frac{y}{x} = \frac{π}{2} - \frac{x}{y} + 2 πn, - \frac{y}{x} = π - (\frac{π}{2} - \frac{x}{y}) + 2 πn

- (\frac{y}{x}) = \frac{π}{2} - \frac{x}{y} + 2 πn : x = - \frac{- π y - 4 πn y + ( π y + 4 πn y ) ^{2} + 16 y ^{2}}{4}, x = - \frac{- π y - 4 πn y - ( π y + 4 πn y ) ^{2} + 16 y ^{2}}{4}

- (\frac{y}{x}) = π - (\frac{π}{2} - \frac{x}{y}) + 2 πn : x = \frac{- π y - 4 πn y + ( π y + 4 πn y ) ^{2} - 16 y ^{2}}{4}, x = \frac{- π y - 4 πn y - ( π y + 4 πn y ) ^{2} - 16 y ^{2}}{4}

x = - \frac{- π y - 4 πn y + ( π y + 4 πn y ) ^{2} + 16 y ^{2}}{4}, x = - \frac{- π y - 4 πn y - ( π y + 4 πn y ) ^{2} + 16 y ^{2}}{4}, x = \frac{- π y - 4 πn y + ( π y + 4 πn y ) ^{2} - 16 y ^{2}}{4}, x = \frac{- π y - 4 πn y - ( π y + 4 πn y ) ^{2} - 16 y ^{2}}{4}

sin (2 t) cos (t) = 0, 0 \leq t \leq π

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

θ, y = 4 sin (θ)

- 3 (sin^{2} (θ) - cos^{2} (θ)) = 0

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

What is the general solution for solvefor x,sin(y/x)+cos(x/y)=0 ?
The general solution for solvefor x,sin(y/x)+cos(x/y)=0 is