1.

If `cosy=xcos(a+y),`with `cosa!=+-1,`provethat`(dy)/(dx)=(cos^2(a+y))/(sina)dot`

Answer» `cosy=x cos(a+y)`
`impliesx=(cosy)/(cos(a+y))`
Differentiate both sides w.r.t. y
`(dy)/(dx)=(cos(a+y)(d)/(dx)cosy-cosy(d)/(dy)cos(a+y))/([cos(a+y)]^(2))`
`=(-cos(a+y)siny+cosysin(a+y))/(cos^(2)(a+y))`
`=(sin(a+y-y))/(cos^(2)(a+y))=(sina)/(cos^(2)(a+y))`
`implies(dy)/(dx)=(cos^(2)(a+y))/(sina) " " `[Hence Proved.


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