Question

If $x>0$ and $co{s}^{-1}\left(\frac{12}{x}\right)+co{s}^{-1}\left(\frac{35}{x}\right)=\frac{\pi }{2},$ then x is

• A. $7$
• B. $39$
• C. $37$
• D. $-37$

Answer 1

The correct option is C $37$

$co{s}^{-1}\left(a\right)+co{s}^{-1}\left(b\right)=\frac{\pi }{2}$
$\Rightarrow co{s}^{-1}\left(a\right)=\frac{\pi }{2}-co{s}^{-1}\left(b\right)$
$\Rightarrow co{s}^{-1}\left(a\right)=si{n}^{-1}\left(b\right)$
Therefore, $a^2+b^2=1$
Substituting the value of a and b we get
${\frac{12}{x}}^2+{\frac{35}{x}}^2=1$
$x^2=1369$
$x=37,-37$
However , since $x>0$
$x=37$