# Chapter 5 - Section 5.2 - Sum and Difference Formulas - Exercise Set - Page 669: 25

The expression $\sin 25{}^\circ \cos 5{}^\circ +\cos 25{}^\circ \sin 5{}^\circ$ is written as $\sin 30{}^\circ$ and the exact value of $\sin 30{}^\circ$ is $\frac{1}{2}$.

#### Work Step by Step

Use the sum formula of sines and rewrite the expression as the sum of angles to obtain the sine of the angle as, \begin{align} & \sin \left( 25{}^\circ +5{}^\circ \right)=\sin 25{}^\circ \cos 5{}^\circ +\cos 25{}^\circ \sin 5{}^\circ \\ & \sin \left( 30{}^\circ \right)=\sin 25{}^\circ \cos 5{}^\circ +\cos 25{}^\circ \sin 5{}^\circ \end{align} Therefore, the expression $\sin 25{}^\circ \cos 5{}^\circ +\cos 25{}^\circ \sin 5{}^\circ$ is equivalent to $\sin 30{}^\circ$. From the knowledge of trigonometric ratios defined for sine of an angle, the exact value of $\sin 30{}^\circ$ is $\frac{1}{2}$.

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