The correct option is D √( 3 ) +1 2√( 2 ) sin (75^∘)= sin (45^∘+30^∘) = sin 45^∘cos 30^∘+ sin 30^∘cos 45^∘ (sin (A+B))= (sin A cos B + cos A si ...

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Sin(A+B)Sin(A-B)

The value of ...

Question

The value of $sin 75^{o} =$

\frac{2 - \sqrt{3}}{\sqrt{2}}

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\frac{\sqrt{3} + 1}{2 \sqrt{2}}

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\frac{\sqrt{3} - 1}{2 \sqrt{2}}

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\frac{\sqrt{3} + 1}{\sqrt{2}}

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Solution

The correct option is D $\frac{\sqrt{3} + 1}{2 \sqrt{2}}$
$sin (75^{\circ}) = sin (45^{\circ} + 30^{\circ})$
$= sin 45^{\circ} cos 30^{\circ} + sin 30^{\circ} cos 45^{\circ} (sin (A + B)) = (sin A cos B + cos A sin B)$
$= \frac{1}{\sqrt{2}} \times \frac{\sqrt{3}}{2} + \frac{1}{2} \times \frac{1}{\sqrt{2}}$
$= \frac{\sqrt{3}}{2 \sqrt{2}} + \frac{1}{2 \sqrt{2}}$
$= \frac{\sqrt{3} + 1}{2 \sqrt{2}}$

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