What is the general solution for solvefor x,cos(3y)=tan(2x) ?

The general solution for solvefor x,cos(3y)=tan(2x) is x=(arctan(cos(3y)))/2+(pin)/2

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solvefor x,cos(3y)=tan(2x)

solvefor

x = \frac{arctan ( cos ( 3 y ) )}{2} + \frac{πn}{2}

Solution steps

cos (3 y) = tan (2 x)

Switch sides

tan (2 x) = cos (3 y)

Apply trig inverse properties

tan (2 x) = cos (3 y)

General solutions for

tan (2 x) = cos (3 y)

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

2 x = arctan (cos (3 y)) + πn

2 x = arctan (cos (3 y)) + πn

Solve

2 x = arctan (cos (3 y)) + πn : x = \frac{arctan ( cos ( 3 y ) )}{2} + \frac{πn}{2}

2 x = arctan (cos (3 y)) + πn

Divide both sides by

2

2 x = arctan (cos (3 y)) + πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arctan ( cos ( 3 y ) )}{2} + \frac{πn}{2}

Simplify

x = \frac{arctan ( cos ( 3 y ) )}{2} + \frac{πn}{2}

x = \frac{arctan ( cos ( 3 y ) )}{2} + \frac{πn}{2}

x = \frac{arctan ( cos ( 3 y ) )}{2} + \frac{πn}{2}

What is the general solution for solvefor x,cos(3y)=tan(2x) ?
The general solution for solvefor x,cos(3y)=tan(2x) is x=(arctan(cos(3y)))/2+(pin)/2