If `sin^(-1)a+sin^(-1)b+sin^(-1)c=pi,` then the value of `asqrt((1-a^2))+bsqrt((1-b^2))+csqrt((1-c^2))` will be (A) `2a b c` (B) `a b c` (C) `1/2a b c` (D) `1/3a b c`

Explanation

`sin^(-1)a=A,sinA=a`

`sin^(-1)b=B,sinB=b`

`sin^(-1)c=C,sinC=c`

`A+B+C=pi`

`sin2A+sin2B+sin2C=4sinAsinBsinC`

`sinAcosA+sinBcosB+sinCcosC=2sinAsinBsinC`

`sinAsqrt(1-sin2B)+sinBsqrt(1-sin2B)+sinCsqrt(1-sin2C)=2sinAsinBsinC`

`asqrt(1-a^2)+bsqrt(1-b^2)+csqrt(1-c^2)=2abc`

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