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MISCELLANEOUS EXAMPLESIf sín.1 x + sin-1 y + sin-1 z = π, prove that

Answer»

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-X^2) +Yv(1-Y^2) +Zv(1-Z^2)=sinA v(1-sin^2A)+sinBv(1-sin^2B) +sinCv(1-sin^2C)

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

=1/2[sin2A+sin2B+sin2C]

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

=2sinAsinBsinC

=2xyz


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