A) \[abc\]
B) \[a+b+c\]
C) \[\frac{1}{a}\times \frac{1}{b}\times \frac{1}{c}\]
D) \[2abc\]
Correct Answer: D
Solution :
[d] Let \[{{\sin }^{-1}}a=x\] \[\therefore a=\sin x\] \[{{\sin }^{-1}}b=y\] \[\therefore b=\sin y;{{\sin }^{-1}}c=z\] \[\therefore c=\sin z\] \[\therefore a\sqrt{1-{{a}^{2}}}+b\sqrt{1-{{b}^{2}}}+c\sqrt{1-{{c}^{2}}}\] \[=\sin x\cos x+\sin y\cos y+\operatorname{sinzcosz}\] \[=(1/2)(sin2x+sin2y+sin2z)=(1/2)(4sinxsinysinz)\]\[=2\sin x\sin y\sin z=2abc\]
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