Question

evalute sin( 2sin-1(0.6)) ​

Answer 1

$\;\;\underline{\textbf{\textsf{ Given:-}}}$

• $\bf\sin \{2\sin^{ - 1}(0.6) \}$

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$\;\;\underline{\textbf{\textsf{ To Find :-}}}$

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• Value of $\bf\sin \{2\sin^{ - 1}(0.6) \}$

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$\;\;\underline{\textbf{\textsf{ Solution :-}}}$

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$\underline{\:\textsf{ Let the function be :}}$

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$\bf \dashrightarrow y = \sin \{2\sin^{ - 1}(0.6) \}$

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$\underline{\:\textsf{ As we know that :}}$

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$\bf \dashrightarrow 2\sin^{ - 1}(x) = { \sin }^{ - 1}(2x \sqrt{1 - {x}^{2} })$

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$\underline{\:\textsf{ Therefore :}}$

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$\bf \dashrightarrow y = \sin \{\sin^{ - 1} \{2(0.6) \sqrt{1 - {(0.6)}^{2} } \} \}$

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$\bf \dashrightarrow y = \sin \{\sin^{ - 1} \{(1.2) \sqrt{1 - 0.36 } \} \}$

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$\bf \dashrightarrow y = \sin \{\sin^{ - 1} \{(1.2) \sqrt{0.64}\} \}$

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$\bf \dashrightarrow y = \sin \{\sin^{ - 1} \{(1.2) \sqrt{0.8 \times 0.8}\} \}$

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$\bf \dashrightarrow y = \sin \{\sin^{ - 1} \{(1.2) (0.8) \}$

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$\bf \dashrightarrow y = \sin \{\sin^{ - 1} \{(0.96) \}$

ㅤ$\;\;\underline{\textbf{\textsf{ Hence-}}}$

$\underline{\textsf{ Value of y is \textbf{0.96 }}}.$

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Answer 2

Step-by-step explanation:

we have

sin2sin^-1 *X=sin^-1(2X√1-X^2)

so ,

sin(sin^-1(2*0.6√1-0.6^2)

=sin(sin^-10.96)

=0.96

is the correct answer...

hope it helps you....