YOU SAID:

\sin\left(\sin\left(x\right)+\cos\left(y\right)\right)=\cos\left(\sin(xy)+\cos x\right)

INTO JAPANESE

\sin\left (\sin\left (x\right) + \cos\left (y\right) \right) = \cos\left (\sin (xy) + \cos x\right)

BACK INTO ENGLISH

\sin\left (\sin\left (x \right) + \cos\left (y \right) \right) = \cos\left (\sin (xy) + \cos x \right)

INTO JAPANESE

\sin\left (\sin\left (x \right) + \cos\left (y \right) \right) = \cos\left (\sin (xy) + \cos \right x)

BACK INTO ENGLISH

\sin\left (\sin\left (x \right) + \cos\left (y \right) \right) = \cos\left (\sin (xy) + \cos x \right)