Question

If
$\small{sin^{-1}x+sin^{-1}y+sin^{-1}z=\frac{\pi}{2}}$ ,
show that $x^{2}+y^{2}+z^{2}+2xyz=1.$​

Answer 1

$\huge \mathfrak \red{answer}$

Formula's I Used! :)

$\sin^{ - 1} (x) = \frac{\pi}{2} - \cos^{ - 1} (x)$

$cos^{ - 1} (x) + cos^{ - 1} (y) =cos^{ - 1} (xy - \sqrt{1 - y^{2} } \times \sqrt{1 - {x}^{2} } )$

$\pi - cos^{ - 1} (x) = cos^{ - 1} ( - x)$

$\huge \mathfrak {\bf {\fbox{ \red{thanks}}}}$