Question

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

(a) (1 – y^2)(1 – Cos^2 (y))=1

(b) (1 – y^2)(1 – Cos(y))=1

(c) (1 – y^2)(1 – Sin^2 (y))=1

(d) (1 – y^2)(1 – Sin(y))=1

This question was addressed to me in examination.

This intriguing question comes from Implicit Differentiation in division Partial Differentiation of Engineering Mathematics

Answer 1

Correct answer is (a) (1 – y^2)(1 – Cos^2 (y))=1

The explanation: Cos(y)=Cos^(-1) (y)

Differentiating both sides

-Sin(y) = \(-\frac{1}{\sqrt{1-y^2}}\)

(1 – y^2)(1 – Cos^2 (y)) = 1.