If `sin^(-1)a+sin^(-1)b+sin^(-1)c=pi,` then `asqrt(1-a^2)+bsqrt(1-b^2)+csqrt(1-c^2)` is equal to `a+b+c` (b) `a^2b^2c^2` `2a b c` (d) `4a 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`.