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• Trigonometry
• Trigonometric identities test
• Sum and Difference Formulas

# Sum and Difference Formulas

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•  Question 1: 1 pts Which identity is this? $$\cos\alpha\cos\beta-\sin\alpha\sin\beta$$
 $sin(\alpha + \beta)$ $sin(\alpha - \beta)$ $cos(\alpha + \beta)$ $cos(\alpha - \beta)$
•  Question 2: 1 pts Which identity is this? $$\sin\alpha\cos\beta-\cos\alpha\sin\beta$$
 The sine of angle alpha plus angle beta. The sine of angle alpha minus angle beta. The cosine of angle alpha plus angle beta. The tangent of angle alpha plus angle beta.
•  Question 3: 1 pts $\sin20^{\circ}\cdot\cos10^{\circ}+\cos20^{\circ}\cdot\sin10^{\circ}=sin(30^{\circ})=\dfrac{1}{2}$
•  Question 4: 1 pts $\cos \dfrac{7\pi}{10}\cdot \cos\dfrac{\pi}{5}+\sin \dfrac{7\pi}{10}\cdot \sin \dfrac{\pi}{5}=1$
•  Question 5: 2 pts Use the angle sum identity to find the exact value of $\cos 105^{\circ}.$
 $\dfrac{\sqrt{2}+\sqrt{6}}{4}$ $\dfrac{-\sqrt{2}-\sqrt{6}}{4}$ $\dfrac{\sqrt{2}-\sqrt{6}}{4}$ none of these
•  Question 6: 2 pts If $\tan\alpha=-\dfrac{3}{4}$ and $\alpha \in \left(\dfrac{\pi}{2}, \pi\right)$ then find the value of $\sin \left(\dfrac{\pi}{4}+\alpha\right).$
 $-\dfrac{4}{5}$ $\dfrac{3}{5}$ $-\dfrac{\sqrt{2}}{10}$ $-\dfrac{7\sqrt{2}}{10}$
•  Question 7: 2 pts If $\sin \alpha=\sin\beta=\dfrac{5}{13}$ and $\alpha \in \left(0, \dfrac{\pi}{2}\right); \beta \in \left(\dfrac{\pi}{2},\pi\right)$ then find the value of $\cos(\alpha+\beta).$
$\cos(\alpha+\beta)=$
•  Question 8: 2 pts Use the angle difference identity to find $\cos(x-\pi).$
 $\cos x$ $-\cos x$ $\sin x$ $-\sin x$
•  Question 9: 3 pts Simplify the expression.
$(\sin x+\sin y)^{2}+(\cos x+ \cos y)^{2}=$
•  Question 10: 3 pts Simplify the expression.
$\dfrac{\sin{\dfrac{\pi}{7}}\cos\dfrac{2\pi}{7}+\cos\dfrac{\pi}{7}\sin\dfrac{2\pi}{7}}{\cos\dfrac{\pi}{7}\cos\dfrac{\pi}{14}+\sin\dfrac{\pi}{7}\sin\dfrac{\pi}{14}}=$
•  Question 11: 3 pts Simplify the expression.
$\cos \left(\dfrac{\pi}{3}-\alpha\right)=$
•  Question 12: 3 pts If $\tan \alpha=\dfrac{1}{7}$ and $\alpha+\beta=\dfrac{\pi}{4}$ find $\tan \beta.$
$\tan \beta=$