Question

The no. of pair of solutions (x, y) of equation

1+ x² + 2x sin (cos^–1y) = 0 is/are

• A. 4
• B. 3
• C. 2
• D. 1

Answer 1

Answer: (D)

1

Answer 2

Q The given equation can be written as

$\frac{x + \frac{1}{x}}{2}$= – sin (cos^–1y) (x ¹ 0)

\ x +$\frac{1}{x}$ ³ 2 or x +$\frac{1}{x}$ £ – 2

\ L.H.S. = R.H.S. if sin (cos^–1 y) = ±1 i.e. x = ±1

When x = –1 sin (cos^–1y) =1

̃ y = 0 as 0 £ cos^–1 y £ p

When x = 1 sin(cos^–1y) = –1

Not possible as 0 £ cos^–1 y £ p

\ x = –1, y = 0 is only solution.