Value of: sin 75^{circ}

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3.Trigonometrical Ratios, Functions and Identities

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Find the value of:

$\sin 75^{\circ}$

A

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

B

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

C

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

D

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

Solution

$\sin 75^{\circ}=\sin \left(45^{\circ}+30^{\circ}\right)$

$=\sin 45^{\circ} \cos 30^{\circ}+\cos 45^{\circ} \sin 30^{\circ}$

$[\sin (x+y)=\sin x \cos y+\cos x \sin y]$

$=\left(\frac{1}{\sqrt{2}}\right)\left(\frac{\sqrt{3}}{2}\right)+\left(\frac{1}{\sqrt{2}}\right)\left(\frac{1}{2}\right)$

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

Standard 11

Mathematics

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