The number of pair solution (x, y) of the equation 1 + x 2 …

Maths Inverse Trigonometric Functions Inverse Trigonometric Functions, Inverse Trigo Identities Numeric Response

Published by: CGP EDU Academic Team

Published on: August 13, 2026

The number of pair solution (x, y) of the equation 1 + x 2 + 2x sin (cos –1 y) = 0 is ……….

Text Solution

Verified by Experts

The correct answer is:

(1)

sin (cos –1 y) = ; x ≠ 0 only possibility is

sin (cos –1 y) = ± 1 & hence x = ± 1

if x = 1 ⇒ sin (cos –1 y) = – 1

⇒ Not Possible [  0 ≤ cos –1 y ≤ π ]

if x = – 1 ⇒ sin (cos –1 y) = 1

⇒ y = 0

So x = –1 & y = 0 is solution

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