  ### Home > PC3 > Chapter Ch8 > Lesson 8.3.5 > Problem8-151

8-151.

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. Then simplify each of the expressions below. 1. $\sin(50^\circ)\cos(20^\circ)+\cos(50^\circ)\sin(20^\circ)$

Use the angle sum formula for sine.

1. $2\sin\left(\frac{2\pi}{5}\right)\cos\left(\frac{2\pi}{5}\right)$

Use the Double-Angle formula for the sine.

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

1. $\cos^2\left(\frac{\pi}{7}\right)-\sin^2\left(\frac{\pi}{7}\right)$

Use the Double-Angle formula for the cosine.

1. $\cos(110^\circ)\cos(50^\circ)-\sin(110^\circ)\sin(50^\circ)$

Use the angle sum formula for the cosine.

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

Use the Half-Angle formula for cosine.

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

Use the Half-Angle formula for sine.