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If (sinx)^y=(cosy)^x ,prove that (dy)/(d...

If `(sinx)^y=(cosy)^x` ,prove that `(dy)/(dx)=(logcosy-ycotx)/(logsinx+xtany)`

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We have, `(sin x)^{y}=(cos y)^{x}`

Taking log on both sides,

`log (sin x)^{y}=log (cos y)^{x} `

`Rightarrow y log (sin x)=x log (cos y)`

Differentiating with respect to `x`,

...
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