Question

If tan^–1 x + cos^–1$\frac{y}{\sqrt{1 + y^{2}}}$= sin^–1$\frac{3}{\sqrt{10}}$where x and y are +ve

integer, then number of possible pair of (x, y) is-

• A. 1
• B. 2
• C. 3
• D.

Answer 1

Answer: (B)

2

Answer 2

tan^–1 x + tan^–1 $\frac{1}{y}$= tan^–1 3

̃ $\frac{xy + 1}{y - x}$= 3 or, y = $\frac{3x + 1}{3 - x}$

y > 0 ̃ $\frac{3x + 1}{3 - x}$> 0

̃ – $\frac{1}{3}$< x < 3

\ x = 1, 2 and corresponding values of y are 2, 7. Hence two pairs (1, 2) and (2, 7) are possible.