# Find dy/dx if x=sinФ-cosФ y=sinФ+cosФ

2
by Sajith

2014-07-29T00:06:37+05:30
X=sinФ-cosФ
y=sinФ+cosФ
dx/dФ = cosФ+sinФ
dy/dФ = cosФ-sinФ
dy/dx = (cosФ-sinФ)/(cosФ+sinФ)
2014-07-29T09:21:42+05:30

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x=sinФ-cosФ
Differentiating w.r.t '
Ф'
dx/dФ = cosФ + sinФ

y=sinФ+cosФ
Differentiating w.r.t. 'Ф'
dy/dФ = cosФ - sinФ

Now,
dy/dx = dy/dФ × dФ/dx
dy/dx = (cosФ-sinФ) × 1/(cosФ+sinФ)
dy/dx = (cosФ-sinФ)/(cosФ+sinФ)

Now you can rationalize,
dy/dx = (cosФ-sinФ)²/1
dy/dx = (cosФ-sinФ)²
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