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• Trigonometry
• Trigonometric identities test
• Product to sum formulas

# Product to sum formulas

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•  Question 1: 1 pts Find the correct formula and express $$\cos u\cdot \sin v$$ as a sum or difference of trigonometric functions
 $\dfrac{1}{2}[\cos (u+v)-\sin(u-v)]$ $\dfrac{1}{2}[\sin (u+v)-\sin(u-v)]$ $\dfrac{1}{2}[\sin (u+v)-\cos(u-v)]$
•  Question 2: 1 pts Express $\sin 3x\cdot \sin 5x$ as a sum or difference of trigonometric functions.
 $\sin 3x\cdot \sin 5x = \dfrac{1}{2}\cos 2x-\dfrac{1}{2}\cos8x$ $\sin 3x\cdot \sin 5x = \dfrac{1}{2}\sin 2x-\dfrac{1}{2}\cos8x$ $\sin 3x\cdot \sin 5x = \dfrac{1}{2}\sin 2x-\dfrac{1}{2}\sin8x$
•  Question 3: 1 pts Express $\sin(\alpha-\beta)\cdot \cos(\alpha+\beta)$ as a sum or difference of trigonometric functions.
 $\dfrac{1}{2}\cos 2\alpha+\dfrac{1}{2}\cos 2\beta$ $\dfrac{1}{2}\cos 2\alpha-\dfrac{1}{2}\sin 2\beta$ $\dfrac{1}{2}\sin 2\alpha+\dfrac{1}{2}\sin 2\beta$ $\dfrac{1}{2}\sin 2\alpha-\dfrac{1}{2}\sin 2\beta$
•  Question 4: 2 pts $$\sin(60^{\circ}-\alpha)\cdot \sin(60^{\circ}+\alpha)=\dfrac{1}{4}\left(2\cos2\alpha+1\right)$$
•  Question 5: 2 pts Find the exact value of the expression.
$\tan 20^{\circ}\cdot \tan 40^{\circ} \cdot \tan 80^{\circ}=$
•  Question 6: 2 pts Express $4\sin\left(1+\dfrac{\pi}{6}\right)\cos\left(1+\dfrac{\pi}{3}\right)$ as a sum or difference of trigonometric functions.
 $\cos 2-1$ $2\cos 2-1$ $2\cos 2+1$ $\cos 2+1$
•  Question 7: 2 pts Express $\cos \dfrac{x}{2}\cos \dfrac{y}{2}\cos \dfrac{x+y}{2}$ as a sum or difference of trigonometric functions.
 $\dfrac{1}{4}+\dfrac{1}{4}\cos x+\dfrac{1}{4} \cos y+ \dfrac{1}{4}\cos (x+y)$ $\dfrac{1}{4}\cos x+\dfrac{1}{4} \cos y+ \dfrac{1}{4}\cos (x+y)$ $\dfrac{1}{4}+\dfrac{1}{4}\cos x+\dfrac{1}{4} \cos y$ $\dfrac{1}{4}+ \dfrac{1}{4}\cos (x+y)$
•  Question 8: 3 pts Simplify the expression using product to sum formulas.
$\sin20^{\circ}\sin 40^{\circ}\sin 60^{\circ}\sin 80^{\circ}=$
•  Question 9: 3 pts $N$ is an integer in the range $[0,180]$ such that $$2\cos43^{\circ}\cos26^{\circ}= \cos69^{\circ}+\cos N.$$ What is the value of $N$?
 $\cos 20^{\circ}$ $\cos 17^{\circ}$ $\cos 27^{\circ}$
•  Question 10: 3 pts Express $4\sin \alpha \sin 2\alpha \sin 4\alpha$ as a sum or difference of trigonometric functions.
 $\sin 2\alpha+\sin 4\alpha+\sin 6\alpha$ $\sin 2\alpha+\sin 4\alpha-\sin 6\alpha$ $\sin 2\alpha-\sin 4\alpha-\sin 6\alpha$ $\sin 3\alpha-\sin 6\alpha-\sin 9\alpha$