Question

If sin inverse x + sin inverse y + sin inverse z is equal to pi then prove that

Answer 1

Let sin-1x =A then x= sinA

Let sin-1y=B then y =sinB

Let sin-1z=C then z=sinC

Then A+B+C =p

Xv(1-X2) +Yv(1-Y2) +Zv(1-Z2)=sinA v(1-sin2A)+sinBv(1-sin2B) +sinCv(1-sin2C)

=sinA.cosA+sinB.cosB+sinC.cosC

=1/2[sin2A+sin2B+sin2C]

=1/2 [4sinA.sinB.sinC]

=2sinAsinBsinC

=2xyz