Question

Find dy/dx. if, x= a(cosϴ + ϴSinϴ) and y= a(sinϴ- ϴcosϴ)​

Answer 1

Answer:

dy/dx = tanθ

Step-by-step explanation:

x = a(cosθ + θsinθ)

differentiate with respect to θ,

dx/dθ = d{a(cosθ + θsinθ)}/dθ

= a[d(cosθ)/dθ + d(θsinθ)/dθ]

= a[ -sinθ + θ.cosθ + sinθ]

= aθ.cosθ ........(1)

again, y = a(sinθ - θ.cosθ)

differentiate with respect to θ,

dy/dθ = d{a(sinθ - θcosθ)}/dθ

= a[dsinθ/dθ - d(θ.cosθ)/dθ ]

= a[cosθ - θ(-sinθ) - cosθ ]

= a[ cosθ + θsinθ - cosθ]

= aθ.sinθ ...........(2)

now, dy/dx = {dy/dθ}/{dx/dθ}

= aθ.sinθ/aθ.cosθ

= tanθ

hence, dy/dx = tanθ

Answer 2

Refer to this attachment.

This attachment will help you