Find the value of: sin 75^{circ} | vedclass

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Question

(A) We know that $\sin 75^{\circ} = \sin (45^{\circ} + 30^{\circ})$.Using the identity $\sin (x + y) = \sin x \cos y + \cos x \sin y$:$\sin (45^{\circ

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) We know that $\sin 75^{\circ} = \sin (45^{\circ} + 30^{\circ})$.Using the identity $\sin (x + y) = \sin x \cos y + \cos x \sin y$:$\sin (45^{\circ} + 30^{\circ}) = \sin 45^{\circ} \cos 30^{\circ} + \cos 45^{\circ} \sin 30^{\circ}$.Substituting the values $\sin 45^{\circ} = \frac{1}{\sqrt{2}}$,$\cos 30^{\circ} = \frac{\sqrt{3}}{2}$,$\cos 45^{\circ} = \frac{1}{\sqrt{2}}$,and $\sin 30^{\circ} = \frac{1}{2}$:$= (\frac{1}{\sqrt{2}})(\frac{\sqrt{3}}{2}) + (\frac{1}{\sqrt{2}})(\frac{1}{2})$$= \frac{\sqrt{3}}{2 \sqrt{2}} + \frac{1}{2 \sqrt{2}}$$= \frac{\sqrt{3} + 1}{2 \sqrt{2}}$.

Find the value of: $\sin 75^{\circ}$

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