If sin-1x+sin-1y+sin-1z+sin-1t=2π, then find the value of x2 + y2 + z2 + t2 - Maths -

Question

If sin - 1 x + sin - 1 y + sin - 1 z + sin - 1 t = 2 π , then
find the value of x 2 + y 2
+ z 2 + t 2

Global Expert · Accepted Answer

We know that the maximum value of
sin-1x, sin-1y, sin-1z and sin-1t isπ2
Now,
LHS=sin-1x+sin-1y+sin-1z+sin-1t        =π2+π2+π2+π2        =2π=RHS
Now,
sin-1x=π2, sin-1y=π2, sin-1z=π2 and sin-1t=π2⇒x=sinπ2, y=sinπ2, z=sinπ2 and t=sinπ2⇒x=1, y=1, z=1 and t=1∴x2+y2+z2+t2=1+1+1+1=4

If sin - 1 x + sin - 1 y + sin - 1 z + sin - 1 t = 2 π , then find the value of x 2 + y 2 + z 2 + t 2

If $\sin^{- 1} x + \sin^{- 1} y + \sin^{- 1} z + \sin^{- 1} t = 2 π$ , then find the value of x ² + y ² + z ² + t ²