Question

Find `"dy"/"dx"`, if : x = sinθ, y = tanθ

Answer 1

x = sinθ, y = tanθ
Differentiating x and y w.r.t. x, we get
`"dx"/"dθ" = "d"/"dθ"(sinθ)` = cosθ
and 
`"dy"/"dθ" = "d"/"dθ"(tanθ)` = sec²θ

`"dy"/"dx" = (("dy"/"dθ"))/(("dx"/"dθ")`

= `sec^2θ/cosθ`
= sec³θ.