Question

Evaluate sin 60 degree cos 30 degree +sin 30 degree cos 60 degree.

Answer 1

To evaluate the expression \(\sin 60^\circ \cos 30^\circ + \sin 30^\circ \cos 60^\circ\), we can use the values of the sine and cosine functions for these angles.

1. We know the following values:
- \(\sin 60^\circ = \frac{\sqrt{3}}{2}\)
- \(\cos 30^\circ = \frac{\sqrt{3}}{2}\)
- \(\sin 30^\circ = \frac{1}{2}\)
- \(\cos 60^\circ = \frac{1}{2}\)

2. Now, substitute these values into the expression:

\[
\sin 60^\circ \cos 30^\circ + \sin 30^\circ \cos 60^\circ = \left(\frac{\sqrt{3}}{2}\right)\left(\frac{\sqrt{3}}{2}\right) + \left(\frac{1}{2}\right)\left(\frac{1}{2}\right)
\]

3. Calculate each term:

\[
\sin 60^\circ \cos 30^\circ = \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2} = \frac{3}{4}
\]

\[
\sin 30^\circ \cos 60^\circ = \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}
\]

4. Add the results:

\[
\frac{3}{4} + \frac{1}{4} = \frac{4}{4} = 1
\]

Thus, the value of the expression \(\sin 60^\circ \cos 30^\circ + \sin 30^\circ \cos 60^\circ\) is \(\boxed{1}\).