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If cos y= x cos (a+y), with cos a ne pm ...

If `cos y= x cos (a+y)`, with `cos a ne pm 1`, prove that `(dy)/(dx)=(cos^(2)(a+y))/(sin a)`.

Text Solution

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Given relation is cos y= x cos (a+y). Therefore,
`x=(cos y)/(cos (a+y))`
`(dx)/(dy)=(d)/(dy)(cos y)/(cos (a+y))`
`=(( cos (a+y)(-sin y)-cos y (-sin (a+y)))/(cos^(2) (a+y)))`
`=((-cos (a+y) sin y + cos y sin (a+y))/(cos^(2) (a+y)))`
`=((sin (a+y-y))/(cos^(2)(a+y)))`
`=(sin a)/(cos^(2) (a+y))`
`therefore" "(dy)/(dx)=(cos^(2)(a+y))/(sin a)`
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