Trigonometry Question 7

Which of the following expressions is equal to $(\sin{60^\circ})(\cos{30^\circ})+(\cos{60^\circ})(\sin{30^\circ})$ ?

\cos{(60^\circ-30^\circ)}

\cos{(60^\circ+30^\circ)}

\sin{(60^\circ-30^\circ)}

\sin{(60^\circ+30^\circ)}

\sin{\left(\dfrac{60^\circ+30^\circ}{2}\right)}

Approach 1

If you know the identity, this problem is straightforward:

\sin{(\alpha + \beta)} = \sin{\alpha}\cos{\beta} + \cos{\alpha}\sin{\beta}

Approach 2

You can evaluate the expression with your calculator and compare it with the answer choices.