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

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

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

solve for

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

x = tan (\frac{π}{2} - arctan (y))

Solution steps

arctan (x) + arctan (y) = \frac{π}{2}

Move

arctan (y)

to the right side

arctan (x) + arctan (y) = \frac{π}{2}

Subtract

arctan (y)

from both sides

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

Simplify

arctan (x) = \frac{π}{2} - arctan (y)

arctan (x) = \frac{π}{2} - arctan (y)

Apply trig inverse properties

arctan (x) = \frac{π}{2} - arctan (y)

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

x = tan (\frac{π}{2} - arctan (y))

x = tan (\frac{π}{2} - arctan (y))

2 sin (x) = 2 sin (2 x)

3 cos (2 x) - 1 = 0

2 cos^{2} (x) = 2

0 = - 2 sin (t) - 4 cos (2 t)

cos (θ) + sin (θ + \frac{π}{2}) = 1, 0 \leq θ < 2 π

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