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`

Options

A. a+b+c
B. `a^(2)b^(2)c^(2)`
C. 2abc
D. 4abc

Answer

C

Explanation

Let `A=sin^(-1)a,B=sin^(-1)b` and `C=sin^(-1)C`
we have `A+B+C=pi`.
`asqrt(1-a^(2))+bsqrt(1-b^(2))+csqrt(1-c^(2))`
`=(1)/(2)(sin 2A+sin2B+sin2C)`
`=(1)/(2)(4sin A sin B sin C)=2abc`.