Simplify: ^@ \dfrac{ \sin x - \sin y } { \cos x + \cos y } + \dfrac{ \cos x - \cos y } { \sin x + \ sin y } ^@


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Answer:

^@ 0 ^@

Step by Step Explanation:
  1. ^@ \begin{align} & \dfrac{ \sin x - \sin y } { \cos x + \cos y } + \dfrac{ \cos x - \cos y } { \sin x + \ sin y } \\ = & \dfrac{ (\sin x - \sin y) (\sin x + \sin y) + (\cos x + \cos y) (\cos x - \cos y) } { (\cos x + \cos y) (\sin x + \ sin y) } \\ = & \dfrac{ \sin^2 x - \sin^2 y + \cos^2 x - \cos^2 y } { (\cos x + \cos y) (\sin x + \ sin y) } \\ = & \dfrac{ 1 - 1 } { (\cos x + \cos y) (\sin x + \ sin y) } \space\space\space\space [sin^2\theta + cos^2\theta = 1] \\ = & 0 \end{align}^@

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