`"If "cos y = x cos(a+y)," with "cos a ne pm1," prove that "(dy)/(dx)=(cos^(2)(a+y))/(sin a).`

Explanation

`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.