These expressions look complicated, but they are not if you know your trigonometric identities. Review the addition/subtraction formulas, double-angle formulas, and half-angle formulas in your Tool Kit. Then express each of the problems below in the form $\sin x$ or $\cos x$.

1. $\sin 50° \cos 20° + \cos 50° \sin 20°$

   Hint (a):

   Use the addition formula for sine.
   $\sin \left(50° + 20°\right)$

2. $2 \operatorname { sin } \frac { 2 \pi } { 5 } \operatorname { cos } \frac { 2 \pi } { 5 }$

   Hint (b):

   Use the Double-Angle Formula for the sine.

   Step (b):

   $\text{sin}\left( 2\left( \frac{2\pi}{5} \right) \right)$

3. $\cos110°\cos50°− \sin110°\sin50°$

   Hint (c):

   Use the sum/difference formula for the cosine. Be careful of your sign.

4. $\operatorname { cos } ^ { 2 } \frac { \pi } { 7 } - \operatorname { sin } ^ { 2 } \frac { \pi } { 7 }$

   Hint (d):

   Use one of the Double-Angle Formulas for the cosine.

5. $\sqrt { \frac { 1 + \operatorname { cos } 20 ^ { \circ } } { 2 } }$

   Hint (e):

   Use the Half-Angle Formula for cosine.

6. $\sqrt { \frac { 1 - \operatorname { cos } 20 ^ { \circ } } { 2 } }$

   Hint (f):

   Use the Half-Angle Formula for sine.