If sin-1 x + sin-1 y + sin-1z = π then x √1 -x2 + y √1-y2 + z √1-z2 =

Question

If sin-1 x + sin-1 y + sin-1z = π then x √1 -x2 + y √1-y2 + z √1-z2 =  (A) xyz (B) 2xyz (C) 4xyz (D) 1 + 4xyz

Tardigrade Admin · Accepted Answer

Let sin-1 x = A , sin-1 y = B , sin-1 z =C then A + B+ C = π and then sin2A + sin B + sin2C = 4 sin A sin B sin C 4 ⇒ 2x √1-x2 + 2y √1-y2 + 2 z √1-z2 = 4xyz ⇒ x √1-x2 + y √1-y2 + z √1-z2 = 2xyz

Q. If $sin^{- 1} x + sin^{- 1} y + sin^{- 1} z = π$ then $x 1 - x^{2} + y 1 - y^{2} + z 1 - z^{2} =$

xyz

2xyz

4xyz

1 + 4xyz

Let $sin^{- 1} x = A, sin^{- 1} y = B, sin^{- 1} z = C$ then A + B+ C = $π$ and then
$sin 2 A + sin B + sin 2 C = 4 sin A sin B sin C$
4\ $\Rightarrow 2 x 1 - x^{2} + 2 y 1 - y^{2} + 2 z 1 - z^{2}$
$= 4 x yz$
$\Rightarrow x 1 - x^{2} + y 1 - y^{2} + z 1 - z^{2} = 2 x yz$

Q. If sin−1x+sin−1y+sin−1z=π then x1−x2​+y1−y2​+z1−z2​=

xyz

2xyz

4xyz

1 + 4xyz

Let sin−1x=A,sin−1y=B,sin−1z=C then A + B+ C = π and then sin2A+sinB+sin2C=4sinAsinBsinC 4\ ⇒2x1−x2​+2y1−y2​+2z1−z2​ =4xyz ⇒x1−x2​+y1−y2​+z1−z2​=2xyz

Q. If $sin^{- 1} x + sin^{- 1} y + sin^{- 1} z = π$ then $x 1 - x^{2} + y 1 - y^{2} + z 1 - z^{2} =$

Let $sin^{- 1} x = A, sin^{- 1} y = B, sin^{- 1} z = C$ then A + B+ C = $π$ and then
$sin 2 A + sin B + sin 2 C = 4 sin A sin B sin C$
4\ $\Rightarrow 2 x 1 - x^{2} + 2 y 1 - y^{2} + 2 z 1 - z^{2}$
$= 4 x yz$
$\Rightarrow x 1 - x^{2} + y 1 - y^{2} + z 1 - z^{2} = 2 x yz$