If tan-1-2y-1-2x-1-31-4xy-2x-2y-13-k Find x-y

Consider 2y+1+2x+1√(3)1 (4xy+2x+2y+13) =2x+1√(3)+2y+1√(3)1 (2x(2y+1)+1(2y+1)(√(3))^2) =2x+1√(3)+2y+1√(3)1 (2x+1)√(3)(2y+1)√(3) Now, tan^ 1[2 ...

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Domain and Range of Trigonometric Ratios

If tan-1[2y...

Question

If ${tan}^{- 1} ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \frac{\frac{2 y + 1 + 2 x + 1}{\sqrt{3}}}{1 - (\frac{4 x y + 2 x + 2 y + 1}{3})} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ = k$ Find $x + y$

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{tan}^{- 1} ⎡ ⎣ \frac{\frac{2 y + 1 + 2 x + 1}{\sqrt{3}}}{1 - (\frac{4 x y + 2 x 2 y + 1}{3})} ⎤ ⎦ = k

\frac{d y}{d x} = \frac{x + y + 1}{2 x + 2 y + 3}

x + y + \frac{k}{3} = c e^{3 (x - 2 y)}

k

2^{x} + 2^{y} = 2^{x + y}

\frac{d y}{d x}

α = {tan}^{- 1} (\frac{\sqrt{3} x}{2 y - x}), β = {tan}^{- 1} (\frac{2 x - y}{\sqrt{3} y})

α - β

\frac{x + 2 y + 1}{2 x - y + 1} = 2; \frac{3 x - y + 1}{x - y + 3} = 5

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