The value of $sin$ $105^{0} . sin 75^{0}$ is

\frac{\sqrt{3} + 2}{4}

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

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\frac{\sqrt{3} - 2}{4}

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

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Solution

The correct option is D $\frac{\sqrt{3} + 2}{4}$
The value of $sin 105^{\circ} . sin 75^{\circ} = \frac{1}{2} (2 sin 105^{\circ} . sin 75^{\circ})$

$= \frac{1}{2} [cos (105^{\circ} - 75^{\circ}) - cos (105^{\circ} + 75^{\circ})]$

$= \frac{1}{2} . [cos 30^{\circ} - cos 180^{\circ}]$

$= \frac{1}{2} . [\frac{\sqrt{3}}{2} + 1]$

$= \frac{\sqrt{3} + 2}{4}$

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Similar questions

If $y = \frac{{sin}^{2} 1500^{\circ} + 4 {sin}^{4} 750^{\circ} - 4 {sin}^{2} 750^{\circ} {cos}^{2} 750^{\circ}}{4 - {sin}^{2} 1500^{\circ} - 4 {sin}^{2} 750^{\circ}}$ . Then the value of $9 y$ is ___

y = $\frac{s i n^{2} 1500^{\circ} + 4 s i n^{4} 750^{\circ} - 4 s i n^{2} 750^{\circ} c o s^{2} 750^{\circ}}{4 - s i n^{2} 1500^{\circ} + 4 s i n^{2} 750^{\circ}}$ Find the value of 9y.

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The value of sin 1050.sin750 is

The correct option is D √3+24The value of sin105∘.sin75∘=12(2sin105∘.sin75∘)=12[cos(105∘−75∘)−cos(105∘+75∘)]=12.[cos30∘−cos180∘]=12.[√32+1]=√3+24

The value of $sin$ $105^{0} . sin 75^{0}$ is