General solution of tan or cos of one multiple equal to tan, cot or cos of another

1. A.
   $\theta=\alpha+\frac{n\pi}{2},\ n\in\mathbb{Z}$
2. B.
   $\theta=\alpha+\frac{3n\pi}{2},\ n\in\mathbb{Z}$
3. C.
   $\theta=n\pi+\alpha,\ n\in\mathbb{Z}$
4. D.
   $\theta=\frac{n\pi}{4}+\alpha,\ n\in\mathbb{Z}$

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1. A.
   12
2. B.
   112
3. C.
   3
4. D.
   36

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

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1. A.
   $\dfrac{2n\pi}{7}, n \in Z$
2. B.
   $\dfrac{2n\pi}{5}, n \in Z$
3. C.
   $n\pi, n \in Z$
4. D.
   $\dfrac{4n\pi}{3}, n \in Z$

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1. A.
   $\theta = n\pi \pm \dfrac{\pi}{6}, n \in Z$
2. B.
   $\theta = n\pi \pm \dfrac{\pi}{3}, n \in Z$
3. C.
   $\theta = n\pi \pm \dfrac{\pi}{4}, n \in Z$
4. D.
   $\theta = n\pi \pm \dfrac{\pi}{8}, n \in Z$

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1. A.
   $\theta = \dfrac{n\pi}{6}, n \in Z$
2. B.
   $\theta = \dfrac{n\pi}{3}, n \in Z$
3. C.
   $\theta = \dfrac{n\pi}{2}, n \in Z$
4. D.
   $\theta = n\pi \pm \dfrac{\pi}{3}, n \in Z$

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

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