Solve sums of sines or cosines by sum-to-product

1. A.
   $x=n\pi+\frac{\pi}{4},\,n\in\mathbb{Z}$
2. B.
   $x=2n\pi+\frac{\pi}{4},\,n\in\mathbb{Z}$
3. C.
   $x=n\pi+(-1)^n\frac{\pi}{4},\,n\in\mathbb{Z}$
4. D.
   $x=\frac{n\pi}{2}+\frac{\pi}{8},\,n\in\mathbb{Z}$

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1. A.
   3
2. B.
   4
3. C.
   6
4. D.
   8

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1. A.
   $\frac{\pi}{4},\frac{\pi}{10}$
2. B.
   $\frac{\pi}{6},\frac{\pi}{3}$
3. C.
   $\frac{\pi}{4},\frac{\pi}{12}$
4. D.
   $\frac{\pi}{8},\frac{\pi}{16}$

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1. A.
   $\frac{\pi}{4},\frac{5\pi}{12},\frac{\pi}{2},\frac{2\pi}{3},\frac{3\pi}{4},\frac{8\pi}{9}$
2. B.
   $\frac{2\pi}{9},\frac{\pi}{4},\frac{\pi}{2},\frac{2\pi}{3},\frac{3\pi}{4},\frac{35\pi}{36}$
3. C.
   $\frac{2\pi}{9},\frac{\pi}{4},\frac{\pi}{2},\frac{2\pi}{3},\frac{3\pi}{4},\frac{8\pi}{10}$
4. D.
   $\frac{2\pi}{9},\frac{\pi}{4},\frac{4\pi}{9},\frac{\pi}{2},\frac{3\pi}{4},\frac{8\pi}{9}$

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1. A.
   $\dfrac{(3n+1)\pi}{p-q}$
2. B.
   $\dfrac{(2n+1)\pi}{p \pm q}$
3. C.
   $\dfrac{(n \pm 1)\pi}{p \pm q}$
4. D.
   $\dfrac{(n+2)\pi}{p+q}$

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1. A.
   $1$
2. B.
   $2$
3. C.
   $3$
4. D.
   $4$

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1. A.
   $1 : 1$
2. B.
   $1 : 2$
3. C.
   $2 : 3$
4. D.
   $2 : 1$

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