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• Trigonometry
• Trigonometric identities test
• Sum to product formulas

# Sum to product formulas

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•  Question 1: 1 pts Express $\cos 2\beta -\cos 8\beta$ as a product.
 $\sin 10\beta \sin 6\beta$ $2\sin 10\beta \sin 6\beta$ $2\sin 5\beta \sin 3\beta$ $\sin 5\beta \sin 3\beta$
•  Question 2: 1 pts Express $\sin 10M +\sin 4M$ as a product.
 $-2\sin 7M\cos 3M$ $\sin 7M\cos 3M$ $\dfrac{1}{2} \sin 7M\cos 3M$ $2\sin 7M\cos 3M$
•  Question 3: 1 pts Express $\sin \left(\dfrac{\pi}{4}+\alpha\right)+\sin \left(\dfrac{\pi}{4}-\alpha\right)$ as a product.
 $\sqrt{2}\sin \alpha$ $\sqrt{2}\cos \alpha$ $\cos \alpha$ $\sin \alpha$
•  Question 4: 1 pts $\sin(\alpha+\beta)-\sin(\alpha-\beta)=2\cos \beta \sin\alpha$
•  Question 5: 2 pts Express$\sin 20^{\circ}+\cos 50^{\circ}$ as a product.
 $\cos 40^{\circ}$ $\cos 30^{\circ}$ $\cos 20^{\circ}$ $\cos 10^{\circ}$
•  Question 6: 2 pts Simplify the expression using sum to product formulas.
$\sin 20^{\circ}+ \sin 34^{\circ}+\sin 24^{\circ}+\sin 30^{\circ}=$
•  Question 7: 2 pts Express $\cos \alpha+\cos 3\alpha+\cos 5\alpha+\cos 7\alpha$ as a product.
 $\cos\alpha \cos 2\alpha \cos 4\alpha$ $4\cos\alpha \cos 2\alpha \cos 4\alpha$ $4\cos\alpha \cos 6\alpha \cos 8\alpha$ none of these
•  Question 8: 2 pts $\sin 75^{\circ}+\sin 15^{\circ}=\dfrac{\sqrt{6}}{2}$
•  Question 9: 3 pts Find the exact value of the expression.$$1+\cos x$$
 $2\cos^{2} x$ $2\tan^{2}\left(\frac{x}{2}\right)$ $2\sin^{2}\left(\frac{x}{2}\right)$ $2\cos^{2}\left(\frac{x}{2}\right)$
•  Question 10: 3 pts Find the exact value of the expression.
$$\sec7^{\circ}(\sin 47^{\circ}+\sin 61^{\circ}-\sin 11^{\circ}-\sin25^{\circ})=$$
•  Question 11: 3 pts Find the exact value of the expression.
$\dfrac{\cos 40^{\circ} + \cos 40^{\circ}-\cos 20^{\circ}}{\sin 20^{\circ}}=$
•  Question 12: 3 pts Express as a product. $$\tan 40^{\circ}+\cot 40^{\circ}$$
 $\dfrac{2}{\cos 20^{\circ}}$ $\dfrac{2}{\cos 10^{\circ}}$ $\dfrac{1}{\cos 10^{\circ}}$ $\dfrac{2}{\sin 10^{\circ}}$