Question

The equation of the normal to the curve y = (1 + x)^y + sin^–1(sin²x) at x = 0.

(a) x + y = 2 

(b) x + y = 1 

(c) x – y = 1 

(d) x² – y² = 2

Answer 1

The correct option (b) x + y = 1

Explanation:

y = (1 + x)^y + sin^–1(sin²x)

∴ (dy/dx) = y ∙ (1 + x)^y–1 + [1/√(1 – sin⁴x)] ∙ 2 sinx cosx

given x = 0 ⇒ y = 1

∴ (dy / dx) = (1) + 0 = 1

Equation of normal is (y – 1) = – 1 (x – 0)

i.e.

y – 1 = – x

∴ x + y = 1