$\"\"$

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Re-write the function as

\

$\"\"$

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Consider u = 1+sin(x) ⇒ sin(x) = u - 1

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Apply derivative on each side,

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du = cos(x) dx

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$\"\"$

\

$\"\"$

\

$\"\"$

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Substitute u = 1+sin(x)

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$\"\"$

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Therefore $\"\"$ .

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