Question

If Sin(y)=Sin^(-1) (y) then?

(a) (1-y^2)(1 – Cos^2 y) = 1

(b) (1-y^2)(1 – Sin^2 y) = 1

(c) (1-y^2)(1 – Siny)=1

(d) (1-y^2)(1 – Cosy)=1

This question was posed to me in an online quiz.

I would like to ask this question from Implicit Differentiation topic in division Partial Differentiation of Engineering Mathematics

Answer 1

Right option is (b) (1-y^2)(1 – Sin^2 y) = 1

To explain: Sin(y)=Sin^(-1) (y)

Differentiating both sides

\(Cos(y) \frac{dy}{dx}=\frac{1}{\sqrt{1-y^2}} \frac{dy}{dx}\)

(1-y^2)(1-Sin^2 y)=1