SIN }^{-1}}a=x\] \[\THEREFORE a=\sin x\] \[{{\sin }^{-1}}b=y\] \[\therefore b=\sin y;{{\sin }^{-1}}C=z\] \[\therefore c=\sin z\] \[\therefore a\sqrt{1-{{a}^{2}}}+b\sqrt{1-{{b}^{2}}}+c\sqrt{1-{{c}^{2}}}\] \[=\sin x\cos x+\sin y\cos y+\operatorname{sinzcosz}\] \[=(1/2)(sin2x+sin2y+sin2z)=(1/2)(4sinxsinysinz)\]\[=2\sin x\sin y\sin z=2abc\]

"> 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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If \[{{\sin }^{-1}}a+{{\sin }^{-1}}b+{{\sin }^{-1}}c=\pi ,\] then find the value of\[a\sqrt{1-{{a}^{2}}}+b\sqrt{1-{{b}^{2}}}+c\sqrt{1-{{c}^{2}}}.\]

Joint Entrance Exam - Main (JEE Main) Mathematics in Joint Entrance Exam - Main (JEE Main) 1 year ago

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[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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Posted on 21 Aug 2024, this text provides information on Joint Entrance Exam - Main (JEE Main) related to Mathematics in Joint Entrance Exam - Main (JEE Main). Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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