Question

Solve for x in : sin^-1 (8/x )+ sin^-1( 15/x)=pie/2

Answer 1

sin^-1(8/x) + sin^-1(15/x) = π/2

$\text{but we know,}$
$\boxed{\boxed{\bold{sin^{-1}X+cos^{-1}X=\frac{\pi}{2}}}}$
so, Let sin^-1(15/x) = P
sinP = 15/x
then, cosP = √(x² - 225)/x
P = cos^-1{√(x² - 225)/x}

now, sin^-1(8/x) + cos^-1{√(x² - 225)/x}= π/2
so, 8/x = √(x² - 225)/x
8 = √(x² - 225)
taking square both sides,
64 = x² - 225
x² = 289 => 17²
x = ±17
hence, x = ±17