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Integration by Substitution

√1+sin A-√1-s...

Question

$\sqrt{(1 + s i n A)} - \sqrt{(1 - s i n A)} = - 2 c o s (A / 2)$

A

A

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B

A

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C

A

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D

A

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Solution

The correct option is C
A

$\sqrt{1 + s i n A}$ - $\sqrt{1 - s i n A} = - 2 c o s (\frac{A}{2})$

$\Rightarrow | c o s \frac{A}{2} + s i n \frac{A}{2} | - | c o s \frac{A}{2} - s i n \frac{A}{2} | = - 2 c o s \frac{A}{2}$

$\frac{5 π}{2} < A < \frac{7 π}{2}$

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