Solve tan x + sec x = 2 cos x: number of solutions, solution set or general solution

1. A.
   0
2. B.
   1
3. C.
   2
4. D.
   3

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1. A.
   2
2. B.
   3
3. C.
   0
4. D.
   1

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1. A.
   $\left\{\frac{\pi}{6}, \frac{7\pi}{6}, \frac{3\pi}{2}\right\}$
2. B.
   $\left\{\frac{\pi}{6}, \frac{5\pi}{6}\right\}$
3. C.
   $\left\{\frac{\pi}{6}, \frac{5\pi}{6}, \frac{3\pi}{2}\right\}$
4. D.
   $\left\{\frac{5\pi}{6}, \frac{11\pi}{6}, \frac{3\pi}{2}\right\}$

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

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1. A.
   $\dfrac{\pi}{6},\dfrac{5\pi}{6}$
2. B.
   $\dfrac{\pi}{6},\dfrac{\pi}{20}$
3. C.
   $\dfrac{\pi}{6},\dfrac{2\pi}{3}$
4. D.
   $\dfrac{\pi}{6},\dfrac{\pi}{12}$

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1. A.
   $x = n\pi + (-1)^n\left(\dfrac{\pi}{3}\right), \quad n \in Z$
2. B.
   $x = n\pi + (-1)^{n+1}\left(\dfrac{\pi}{2}\right), \quad n \in Z$
3. C.
   $x = n\pi + (-1)^n\left(\dfrac{\pi}{4}\right), \quad n \in Z$
4. D.
   $x = n\pi + (-1)^n\left(\dfrac{\pi}{6}\right), \quad n \in Z$

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