Question

evalute sin(2sin inverse 0.6​

Answer 1

Question :–

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$\bf \implies Evaluate\:\:\sin \{2\sin^{ - 1}(0.6) \}$

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ANSWER :–

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• Value = 0.96

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EXPLANATION :–

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GIVEN :–

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• $\bf\sin \{2\sin^{ - 1}(0.6) \}$

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TO FIND :–

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• Value = ?

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SOLUTION :–

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• Let the function –

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

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• We know that –

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

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• So that –

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

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

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

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

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

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

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$\bf \implies \large{ \boxed{ \bf y =0.96}}$

Answer 2

$\huge\pink{\underline{\underline{\bf{\blue{Question :–}}}}}$

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$\bf \implies Evaluate\:\:\sin \{2\sin^{ - 1}(0.6) \}$

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$\huge\pink{\underline{\underline{\bf{\blue{Answer:–}}}}}$

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$\pink{Value \ = \ 0.96}$

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$\purple{EXPLANATION :–}$

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$\green{GIVEN :–}$

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

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$\green{To \ FIND :–}$

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$\red{Value \ = \ ?}$

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$\bold\purple{SOLUTION :–}$

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$\red{Let \ the \ function –}$

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

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•$\red{We \ know \ that}$

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

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$\purple{So \ that –}$

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

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

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

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

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

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

$\bf \implies \large{ \boxed{ \bf y =0.96}}$

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