What is the value of $\sin 30^\circ \cos 60^\circ + \cos 30^\circ \sin 60^\circ$?
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Question

What is the value of $\sin 30^\circ \cos 60^\circ + \cos 30^\circ \sin 60^\circ$?

Accepted Answer

Using the trigonometric table values: $\sin 30^\circ = \frac{1}{2}$, $\cos 60^\circ = \frac{1}{2}$, $\cos 30^\circ = \frac{\sqrt{3}}{2}$, and $\sin 60^\circ = \frac{\sqrt{3}}{2}$. Substituting these values into the expression gives: $(\frac{1}{2} 	imes \frac{1}{2}) + (\frac{\sqrt{3}}{2} 	imes \frac{\sqrt{3}}{2}) = \frac{1}{4} + \frac{3}{4} = \frac{4}{4} = 1$. Alternatively, using the identity $\sin(A+B) = \sin A \cos B + \cos A \sin B$, we get $\sin(30^\circ + 60^\circ) = \sin 90^\circ = 1$.

Introduction to Trigonometry

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