Question

The number of positive integral solutions of the equation $ta{n}^{-1}x+co{s}^{-1}\frac{y}{\sqrt{1+y^2}}=si{n}^{-1}\frac{3}{\sqrt{10}}$

• A. one
• B. two
• C. zero
• D. none of these

Answer 1

The correct option is B

two

$ta{n}^{-1}x+ta{n}^{-1}\frac{1}{y}=ta{n}^{-1}3$
or $ta{n}^{-1}\frac{1}{y}=ta{n}^{-1}3-ta{n}^{-1}x$
or $ta{n}^{-1}\frac{1}{y}=ta{n}^{-1}\frac{3-x}{1+3x}$
$\Rightarrow y=\frac{1+3x}{3-x}$
As, x, y are positive integers, x = 1, 2 and corresponding y = 2 , 7
$\therefore$ Solutions are (x, y) = (1, 2), (2, 7)