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

If `sin^(-1)a+sin^(-1)b+sin^(-1)c=pi,` then the value of `asqrt((1-a^2

1.	If `sin^(-1)a+sin^(-1)b+sin^(-1)c=pi,` then the value of `asqrt((1-a^2))+bsqrt((1-b^2))+sqrt((1-c^2))` will be(A) `2a b c`(B) `a b c`(C) `1/2a b c`(D) `1/3a b c`
Answer» `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` Option A is correct.

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