Use the sum-to-product formulas to find the exact value of the given expression.
$\cos 150 ^ { \circ } + \cos 30 ^ { \circ }$
A) $\frac { - \sqrt { 3 } } { 2 }$
B) 1
C) $\frac { \sqrt { 3 } } { 2 }$
D)-1
E)0

Question

Use the sum-to-product formulas to find the exact value of the given expression.  
  $\cos 150 ^ { \circ } + \cos 30 ^ { \circ }$  
A)  $\frac { - \sqrt { 3 } } { 2 }$
B) 1
C)  $\frac { \sqrt { 3 } } { 2 }$
D)-1
E)0

Quizplus · Accepted Answer

The sum-to-product formula for cosines is $\cos A + \cos B = 2 \cos \left( \frac{A + B}{2} \right) \cos \left( \frac{A - B}{2} \right)$. Applying this formula to $\cos 150^\circ + \cos 30^\circ$, we get $2 \cos \left( \frac{150^\circ + 30^\circ}{2} \right) \cos \left( \frac{150^\circ - 30^\circ}{2} \right) = 2 \cos 90^\circ \cos 60^\circ = 2 \cdot 0 \cdot \frac{1}{2} = 0$.

Use the Sum-To-Product Formulas to Find the Exact Value of the Given