The correct option is B 1/√(2)sinA sin^2(π/8+A/2) sin^2(π/8 A/2) =sin[(π/8+A/2)+(π/8 A/2)]sin[(π/8+A/2) (π/8 A/2)] =sinπ/4sinA =1√(2)s ...

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Integration of Irrational Algebraic Fractions - 2

sin2π8+A2-sin...

Question

${sin}^{2} (\frac{π}{8} + \frac{A}{2}) - {sin}^{2} (\frac{π}{8} - \frac{A}{2}) = . . . . . . . . .$

\frac{1}{\sqrt{2}} cos A

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\frac{1}{\sqrt{2}} sin A

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\sqrt{2} sin A

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None of these

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Solution

The correct option is B $\frac{1}{\sqrt{2}} sin A$
${sin}^{2} (\frac{π}{8} + \frac{A}{2}) - {sin}^{2} (\frac{π}{8} - \frac{A}{2})$

$= sin [(\frac{π}{8} + \frac{A}{2}) + (\frac{π}{8} - \frac{A}{2})] sin [(\frac{π}{8} + \frac{A}{2}) - (\frac{π}{8} - \frac{A}{2})]$

$= sin \frac{π}{4} sin A$

$= \frac{1}{\sqrt{2}} sin A$

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