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If sin(a+y)+sina.cos(a+y)=0. Prove that...

If ` sin(a+y)+sina.cos(a+y)=0.` Prove that : `(dy)/(dx)=(sin^2(a+y)/(sina))`

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We have,
`x sin(a+y)+sina.cos(a+y)=0`
`rArr xsin(a+y)=-sina.cos(a+y)`
`rArr x = (-sina.cos(a+y))/(sin(a+y))`
`rArr x = -sina.cot(a+y)`
`:. (dx)/(dy) = - sina.[-cosec^(2)(a+y)].(d)/(dy)(a+y)`
`= sina.(1)/(sin^(2)(a+y)).1`
`= (sin^(2)(a+y))/(sina)`
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