sin 60^{circ} cdot cos 30^{circ} + cos 60^{ci | vedclass

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Question

(A) The given expression is $\sin 60^{\circ} \cdot \cos 30^{\circ} + \cos 60^{\circ} \cdot \sin 30^{\circ}$.We know the trigonometric values: $\sin 60

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(A) The given expression is $\sin 60^{\circ} \cdot \cos 30^{\circ} + \cos 60^{\circ} \cdot \sin 30^{\circ}$.We know the trigonometric values: $\sin 60^{\circ} = \frac{\sqrt{3}}{2}$,$\cos 30^{\circ} = \frac{\sqrt{3}}{2}$,$\cos 60^{\circ} = \frac{1}{2}$,and $\sin 30^{\circ} = \frac{1}{2}$.Substituting these values into the expression:$= (\frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}) + (\frac{1}{2} \cdot \frac{1}{2})$$= \frac{3}{4} + \frac{1}{4}$$= \frac{4}{4} = 1$.Alternatively,using the identity $\sin(A + B) = \sin A \cos B + \cos A \sin B$,where $A = 60^{\circ}$ and $B = 30^{\circ}$:$= \sin(60^{\circ} + 30^{\circ}) = \sin 90^{\circ} = 1$.

$\sin 60^{\circ} \cdot \cos 30^{\circ} + \cos 60^{\circ} \cdot \sin 30^{\circ} = ..........$

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