1. Tardigrade
  2. Question
  3. Mathematics
  4. The number of triplets (x, y, z) satisfies the equation sin-1 x + sin-1 y + sin-1 z = (3 π/2) is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The number of triplets $(x,\, y,\, z)$ satisfies the equation $sin^{-1} x + sin^{-1} y + sin^{-1} z = \frac{3 \pi}{2}$ is

Inverse Trigonometric Functions

Solution:

$sin^{-1}x + sin^{-1}y+sin^{-1} z= \frac{3\pi}{2}$
$\therefore -\frac{\pi }{2} < sin^{-1} x < \frac{\pi }{2}$,
$\frac{-\pi }{2} < sin^{-1} y < \frac{\pi }{2}$
and $\frac{-\pi }{2} < sin^{-1} z < \frac{\pi }{2}$
Hence the above condition satisfies if
$sin^{-1}x = sin^{-1}y = sin^{-1} z = \frac{\pi }{2}$
$\Rightarrow x = y = z = 1$