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Question

Solve dydx=(sinx−siny)cosxcosy.

A
siny=sinx1cesinxsinxcosxdx
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B
siny=sinx1+cesinxsinxcosxdx
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C
siny=sinx1+cesinxsinxcosxdx
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D
siny=sinx1+cesinxsinxcosxdx
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Solution

The correct option is C siny=sinx1+cesinxsinxcosxdx
dydx=(sinxsiny)cosxcosycosydydx+sinycosx=sinxcosx
Put siny=vcosydy=dv
dvdx+vcosx=sinx ...(1)
Here P=cosxPdP=cosxdx=sinx
I.F.=esinx
Multiplying (1) by I.F. we get
esinxdvdx+esinx.vcosx=esinx.sinx
Integrating both sides, we get
v.e.sinx=esinxsinxcosxdx
siny=sinx1+cesinxsinxcosxdx

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