What is the value of frac{[sin (y-z)+sin (y+z | vedclass

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(B) Given expression: $\frac{\sin (y-z)+\sin (y+z)+2 \sin y}{\sin (x-z)+\sin (x+z)+2 \sin x}$Using the trigonometric identity $\sin A + \sin B = 2 \si

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$\frac{\sin y}{\sin x}$

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(B) Given expression: $\frac{\sin (y-z)+\sin (y+z)+2 \sin y}{\sin (x-z)+\sin (x+z)+2 \sin x}$Using the trigonometric identity $\sin A + \sin B = 2 \sin \left( \frac{A+B}{2} \right) \cos \left( \frac{A-B}{2} \right)$:Numerator: $\sin (y-z) + \sin (y+z) + 2 \sin y = 2 \sin y \cos z + 2 \sin y = 2 \sin y (\cos z + 1)$Denominator: $\sin (x-z) + \sin (x+z) + 2 \sin x = 2 \sin x \cos z + 2 \sin x = 2 \sin x (\cos z + 1)$Dividing the numerator by the denominator:$= \frac{2 \sin y (\cos z + 1)}{2 \sin x (\cos z + 1)}$$= \frac{\sin y}{\sin x}$

What is the value of $\frac{[\sin (y-z)+\sin (y+z)+2 \sin y]}{[\sin (x-z)+\sin (x+z)+2 \sin x]} = ?$

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