# Chapter 2 - Test - Page 97: 3

$\theta=15^{\circ}$

#### Work Step by Step

Since sine and cosine are cofunctions, $\sin(\theta+15^{\circ})= cos (2\theta+30^{\circ})$ is true if the sum of the angles is 90°. $(\theta+15^{\circ})+(2\theta+30^{\circ})=90^{\circ}$ $3\theta+45^{\circ}=90^{\circ}$ Subtracting $45^{\circ}$ from each side, $3\theta=45^{\circ}$ Dividing each side by $15$, $\theta=15^{\circ}$

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