Question

sin ^-1 (8/x) + sin ^ -1 (15/x) = π/2



can any one solve it ?​

Answer 1

Answer:

x = ±17

Step-by-step explanation:

sin^-1(8/x) + sin^-1(15/x) = π/2

\text{but we know,}but we know,

\boxed{\boxed{\bold{sin^{-1}X+cos^{-1}X=\frac{\pi}{2}}}}sin−1X+cos−1X=2π

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