Question

find dy/dx if   x=sinФ-cosФ
                   y=sinФ+cosФ

Answer 1

x=sinФ-cosФ
y=sinФ+cosФ
dx/dФ = cosФ+sinФ
dy/dФ = cosФ-sinФ
dy/dx = (cosФ-sinФ)/(cosФ+sinФ)

Answer 2

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