Question

Find `"dy"/"dx"` ; if x = sin³θ , y = cos³θ

Answer 1

x = sin³ θ 

differentlating w.r.t. θ

`"dy"/("d" theta) = 3 "sin"^2 theta . "cos" theta`

Y = cos³θ

Differentiating w.r.t. θ

`"dy"/("d" theta) = 3"cos"^2 theta (-"sin" theta)`

= -3 cos² θ . sin θ

`"dy"/"dx" = ("dy"/("d"theta))/("dx"/("d" theta)) = (-3"cos"^2  theta . "sin"  theta)/(3"sin"^2 theta . "cos"  theta) = ("- cos"  theta)/("sin"  theta) = - "cot"  theta`